
	Where results make sense

Topic: Torsion group

Related Topics

torsion bar

Torsion bar experiment

testicular torsion

torsion balance

torsion free

torsion spring

torsion beam suspension

torsion group

torsion coefficient

Torsion dystonia

Torsion catapult

In the News (Wed 23 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Free abelian group - Wikipedia, the free encyclopedia
		In abstract algebra, a free abelian group is an abelian group that has a "basis" in the sense that every element of the group can be written in one and only one way as a finite linear combination of elements of the basis, with integer coefficients.
		Note a point on terminology: a free abelian group is not the same as a free group that is abelian; in fact the only free groups that are abelian are those of rank 0 (the trivial group) and rank 1 (the infinite cyclic group).
		All free abelian groups are torsion-free, and all finitely generated torsion-free abelian groups are free abelian.
	en.wikipedia.org /wiki/Free_abelian_group (641 words)

	Torsion subgroup -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		The abelian group A is called torsion free if every element of A except the (The distinct personality of an individual regarded as a persisting entity) identity is of infinite order, and torsion (or periodic) if every element of A has finite order.
		Every (additional info and facts about free abelian) free abelian group is torsion free, but the converse is not true, as is shown by the additive group of the (An integer or a fraction) rational numbers Q.
		If A is abelian, then the torsion subgroup T is a (additional info and facts about characteristic subgroup) characteristic subgroup of A (even fully characteristic) and the factor group A/T is torsion free.
	www.absoluteastronomy.com /encyclopedia/t/to/torsion_subgroup.htm (676 words)

	Torsion subgroup - Wikipedia, the free encyclopedia
		In group theory, the torsion subgroup of an abelian group A is the subgroup of A consisting of all elements that have finite order.
		Every free abelian group is torsion free, but the converse is not true, as is shown by the additive group of the rational numbers Q.
		An abelian group A is torsion free if and only if it is flat as a Z-module, which means that whenever C is a subgroup of some abelian group B, then the natural map from the tensor product C ⊗ A to B ⊗ A is injective.
	www.wikipedia.org /wiki/Torsion_subgroup (654 words)

	Rank of an abelian group - Wikipedia, the free encyclopedia
		In mathematics, the rank, or torsion-free rank, of an abelian group measures how large a group is in terms of how large a vector space one would need to "contain" it; or alternatively how large a free abelian group it can contain as a subgroup.
		An abelian group is often thought of as composed of its torsion subgroup T, and its torsion-free part A/T.
		This shows that a single group can have all possible combinations of a given number of building blocks, so that even if one were to know complete decompositions of two torsion-free groups, one would not be sure that they were not isomorphic.
	en.wikipedia.org /wiki/Rank_of_an_abelian_group (665 words)

	PlanetMath: torsion
		the torsion consists only of the identity element.
		Cross-references: finite group, cyclic group, subgroup, abelian, identity element, group
		This is version 2 of torsion, born on 2003-01-07, modified 2003-01-24.
	planetmath.org /encyclopedia/Torsion3.html (61 words)

	PlanetMath: the arithmetic of elliptic curves
		The Tate-Shafarevich group (or ``Sha'') measures the failure of the Hasse principle on the elliptic curve.
		Mazur's theorem on torsion of elliptic curves (a classification of all possible torsion subgroups).
		A way to determine the torsion group: the torsion subgroup of an elliptic curve injects in the reduction of the curve.
	planetmath.org /encyclopedia/ArithmeticOfEllipticCurves.html (547 words)

	testicle, torsion, epididymitis, cremasteric reflex
		The purpose of this study was to compare historical features and physical examination findings among epididymitis, testicular torsion, and torsion of the appendix testis and to determine the reliability of color Doppler ultrasound in diagnosing testicular torsion.
		Testicular torsion is a surgical emergency due to the risk of gonadal loss within 6-8 hours of the torsion.
		Torsion of the appendix testis is more common in the prepubescent male and results in gradual onset of pain, with exquisite tenderness of the upper pole of the testicle.
	rad.usuhs.mil /ms2radpath/testicle.htm (696 words)

	Torsion subgroup - InfoSearchPoint.com (Site not responding. Last check: 2007-10-19)
		In group theory, the torsion subgroup of an abelian group G is the subgroup T of G which consists of all elements of G which have finite order.
		A torsion group need not be finite; for example the direct sum of a countable number of copies of the cyclic group C
		An abelian group G is torsion free if and only if it is flat as a Z-module, which means that whenever K is a subgroup of the abelian group H, then the natural map between the tensor products K ⊗ G and H ⊗ G is injective.
	www.infosearchpoint.com /display/Torsion_group (575 words)

	Torsion subgroup (Site not responding. Last check: 2007-10-19)
		If A and B are abelian groups with torsion subgroups T(A) and T(B), respectively, and f : A → B is a group homomorphism, then f(T(A)) is a subset of T(B).
		An abelian group A is torsion free if and only if it is flat as a Z-module, which means that whenever C is a subgroup of some abelian group B, then the natural map from the tensor product C ⊗ A to B &otimes; A is injective.
		In the case of a finite abelian group A it coincides with the Sylow subgroup for p, and A is up to isomorphism the direct sum of these subgroups.
	www.worldhistory.com /wiki/T/Torsion-subgroup.htm (704 words)

	BACKGROUND
		We also note that two one-relator groups with relators r_1 and r_2 being isomorphic does not imply that r_1 and r_2 are conjugate by an automorphism of a free group, which deprives one from the most straightforward way of attacking this problem; see [J.McCool, A.Pietrowski, On free products with amalgamation of two infinite cyclic groups.
		This implies that the automorphism group Aut(F_2) is NOT rigid.
		Indeed, the group F^Z[x] is discriminated by F [R.Lyndon, Groups with parametric exponents, Trans.
	zebra.sci.ccny.cuny.edu /web/nygtc/problems/Back.html (4533 words)

	Physical Therapy/ Vol 79 No 11/ v79n11p1043 (Site not responding. Last check: 2007-10-19)
		A comparison group of subjects consisted of patients referred for physical therapy for an upper-extremity problem whose diagnosis did not appear to me to indicate that the problem was neck- or back-related (eg, thoracic outlet syndrome).
		The standard error of the innominate torsion measurement was estimated as the square root of the mean square error from the repeated-measures analysis of variance.
		Torsion may have been considered present due to underdevelopment or overdevelopment of one innominate (or of a landmark on the innominate) rather than any disruption in alignment.
	www.ptjournal.org /PTJournal/November1999/v79n11p1043.cfm (9004 words)

	Re: Fundamental group with torsion related to spin, statistics? (Site not responding. Last check: 2007-10-19)
		while the fact that the permutation group S_k shows up in the "statistics" of particles arises from the fact that the fundamental group of the space of unordered k-tuples of distinct points in R^n is S_k when n is 3 or more.
		Witten found an important space with fundamental group equal to Z/24, and this is related to the mysterious importance of the number 24 in string theory, but I won't explain this...
		The group SL(2,C) is the "universal cover" of PSL(2,C) - a double cover, since pi_1(PSL(2,C)) = Z/2 - and this means that it is simply connected.
	www.lns.cornell.edu /spr/2001-10/msg0036219.html (955 words)

	Simple genus-2 Jacobians with rational points of high order
		The constructions hinge on the torsion structure of the elliptic curves whose product is isogenous with J. These are controlled by various ``modular curves'', whose study is an active and highly developed topic in number theory.
		Torsion points of high order are usually constructed by forcing C to have two or three non-Weierstrass points that support several divisors linearly equivalent to zero.
		The N=39 curve is also remarkable for having minimal automorphism group (only the identity and the hyperelliptic involution) and four pairs of non-Weierstrass points, each of which differs from any Weierstrass point by a torsion divisor.
	www.math.harvard.edu /~elkies/g2_tors.html (1731 words)

	PlanetMath:
		Galois group of the compositum of two Galois extensions owned by alozano
		group scheme of multiplicative units (in group scheme of multiplicative units) owned by mathcam
		groups that act freely on trees are free owned by archibal
	planetmath.org /encyclopedia/G (1040 words)

	Research Publication
		Nitro and carboxamide group torsion angles have been determined by O-17 MNR spectroscopy and X-ray crystallography, and one-electron reduction potentials by pulse radiolysis.
		O-17 Chemical shifts indicated similar amide torsion angles (from 35 degrees to 45 degrees) as the alkyl group varied from hydrogen to tert-butyl, but widely differing nitro group torsion angles; from 36 degrees (hydrogen) to 92 degrees (tert-butyl).
		Crystal structures of the isopropyl and tert-butyl derivatives indicate amide group torsion angles (50 degrees and 64 degrees) somewhat larger than those predicted by O-17 NMR, and nitro group torsion angles (59 degrees and 65 degrees respectively) considerably smaller than those predicted by O-17 NMR (75 degrees and 92 degrees respectively).
	www.che.auckland.ac.nz /research/abstract.aspx?pubid=931 (254 words)

	Passman's Abstracts
		Let K[G] be the group algebra of a torsion group G over an infinite field K, and let U=U(G) denote its group of units.
		Specifically, we show that certain basic results which hold when G is a polycyclic-by-finite group with no finite normal subgroups need not hold in the case of group algebras of finite groups.
		Here we begin the analysis in the case where the abelian group A is the additive group of a finite-dimensional vector space V over a locally finite field F of prime characteristic p, and the automorphism group G is a simple infinite absolutely irreducible subgroup of GL(V).
	www.math.wisc.edu /~passman/abstracts.html (3448 words)

	[No title]
		The torsion subgroup is the set of sequences of elements in these groups for which the order of the terms in the sequence stays bounded.
		The existence of a guaranteed splitting is equivalent to the vanishing of the cohomology group H^2(G/T, T), but inasmuch as it is not possible (as far as I know!) to "classify" all torsion-free groups it is unlikely one could hope to compute their cohomology.
		Now the torsion subgroup T(G) is simply the group of all g in G such that g(p)=0 for all except finitely many p.
	www.math.niu.edu /~rusin/known-math/94/split-abel (1283 words)

	[No title]
		Furthermore, G_2 is torsion free (from the general theory of HNN extensions).
		At each step, you can use the HNN extension construction to embed G_k in a group G_{k+1}, in which any two elements of G_k are conjugate provided only that their orders are equal (it may be, however, that two elements of G_{k+1} with infinite orders are not conjugate in G_{k+1}).
		USSR Izvestiya, 29(1987), 233--277) constructed a noncyclic two generator group in which every element is conjugate to a power of the first generator --- but I don't know whether this is a torsion group (so that there would be only finitely many conjugacy classes).
	www.math.niu.edu /~rusin/known-math/95/finite.conj (2102 words)

	IngentaConnect Polynomiality Properties of Group Extensions with a Torsion-Free ... (Site not responding. Last check: 2007-10-19)
		So for investigating nilpotent groups of higher class it is natural to ask for a generalization of this fact, namely when ℤ m is replaced by some torsion-free nilpotent group G and ℤ n by some torsion-free abelian group B with nilpotent G-action.
		In case a given group extension is representable by a polynomial cocycle we also determine the minimal degree of polynomiality for which this holds.
		As applications, it yields an inductive cohomological description of automorphism groups of torsion-free nilpotent groups [9] and a generalization of the classical Dold-Kan equivalence -between simplicial abelian groups and chain complexes of abelian groups-to simplicial groups of class 2.
	www.ingentaconnect.com /content/ap/ja/1996/00000179/00000002/art00017 (722 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		The integral homology groups of SL(F) are in general not finitely generated bu* t, it was shown by the first author in Section 2 of [A1] that, for all integers i 0, Hi (SL(F); Z) is the direct sum of a free abelian group* of finite rank and a torsion group.
		A finiteness theorem The first result on the structure of the integral homology groups of SL(F)* * is given by Theorem 7 of [A1]: for any i 0, Hi(SL(F); Z) is the direct sum of a free * abelian group* of finite rank and a torsion group.
		This i* mplies_that D (i) is contained in the kernel of f], hence, it is finitely generated._Finall y, D (i) is finite because one deduces clearly from the structure of Hi(SL(F); Z) that D (i) is a * torsion group.
	hopf.math.purdue.edu /Arlettaz-Zelewski/homodiv.txt (2411 words)

	[No title]
		The group of homotopy equivalences of products of spheres and of Lie groups Martin Arkowitz and Jeffrey Strom Abstract We investigate the group E# (X) of self homotopy equivalences of a space X which induce the identity homomorphism on all homotopy groups.
		The group E# (X) is a natural subgroup of the group E(X) of all self homotopy equivalences of X. There are essentially two types of results on E(X) and E# (X* ): (1) properties of these groups* for large classes of spaces, and (2) detailed calcul* ations of the group* structure for specific spaces.
		In this section we determine the structu* re of the abelian group* Z# (P) in terms of the homotopy groups of spheres.
	hopf.math.purdue.edu /Arkowitz-Strom/Equivalences.txt (5336 words)

	MedlinePlus Medical Encyclopedia: Testicular infection or torsion (Site not responding. Last check: 2007-10-19)
		Testicular infection or torsion is a group of disorders in which testicular pain is a primary symptom.
		Testicular torsion is a twisting of the spermatic cord, artery and vein, which cuts off the blood supply to the testicle and surrounding structures within the scrotum.
		Testicular torsion is the most common cause of scrotal or testicular pain in boys and non-sexually active adolescents.
	www.nlm.nih.gov /medlineplus/ency/article/001287.htm (546 words)

	ELLIPTIC CURVES IN NATURE (Site not responding. Last check: 2007-10-19)
		A curve with CM (complex multiplication) whose endomorphism ring is generated by (-D+sqrt(-D))/2 is said to have CM-D; for instance the curves with CM-3 and CM-4 are those of j-invariant 0 and 1728 respectively.
		NB the Antwerp tables wrongly give the size of the torsion group of this curve as 4; presumably this entry was switched with the one for 15-A2(E): [1,1,1,-135,-660], where Antwerp says T=8 but in fact T=2*2 (Frey curve for 1+80=81).
		Fermat proved that these curves have no rational points other than their torsion points, using what he famously called his "method of descent", and which is a special case of what we now call a descent via a 2-isogeny, here the 2-isogeny between 32-A1(B) and 32-A2(A).
	modular.fas.harvard.edu /tables/nature (5086 words)

	Torsion subgroup (Site not responding. Last check: 2007-10-19)
		The set T of all elements of finite order in an abelian group indeed forms a subgroup: suppose x and y are in T and m is the product of their orders.
		Every free abelian[?] group is torsion free, but the converse isn't true, as is shown by the additive group of the rational numbers Q.
		If G is abelian, then the torsion subgroup T is a fully characteristic subgroup of G, and the factor group G/T is torsion free.
	www.termsdefined.net /to/torsion-subgroup.html (731 words)

	Subgroups of Modular Abelian Varieties
		The subgroup generated by torsion approximations of a set of generators of the subgroup G of a modular abelian variety.
		Let G be a finitely generated subgroup of an abelian variety A. Return an abstract abelian group H which is isomorphic to G along with isomorphisms in both directions.
		Let G be a finite torsion subgroup of its ambient abelian variety A whose elements are all known exactly, i.e.
	www.math.lsu.edu /magma/text1330.htm (1854 words)

	Lee Lady: Finite Rank Torsion Free Modules over Dedekind Domains (a book)
		In the study of torsion groups, the ring theorist finds more concepts that are strange to him than concepts which are familiar, and this cannot be remedied by a mere change in terminology.
		The theory of finite rank torsion free abelian groups is full of results that depend on countability, or on having characteristic zero, or working over a ring whose quotient field is a perfect field, as well as proofs using quite specialized results from number theory.
		Unlike the theory of torsion groups, the theory of finite rank torsion free modules is becoming something that fits in fairly well with the mainstream of commutative ring theory.
	www.math.hawaii.edu /~lee/book (629 words)

	Atlas: On the Structure of the Group of Units os the Group Ring of a Torsion Group by A.A. Bovdi (Site not responding. Last check: 2007-10-19)
		Let RG be the group ring of a torsion group G over an integral domain R. We denote by U(RG) the group of units of the group ring RG and by V(RG) the subgroup of its normalized units.
		Group algebras have been characterized under different group-theoretical assumption on its group of units, such as being nilpotent, solvable or n-Engel.
		Moreover, this is true for all nilpotent normal subgroup in V(RG) with weaker assumptions about the group G, namely, for any torsion group G with some restriction on RG.
	atlas-conferences.com /c/a/b/w/11.htm (364 words)

Try your search on: Qwika (all wikis)