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Topic: Torsion free

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	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: Definition and Links by Encyclopedian.com - All about Torsion subgroup
		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.
		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 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.encyclopedian.com /to/Torsion-subgroup.html (528 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.
		More generally, the rank of any free abelian group (as explained in that article) coincides with its t.f.
	en.wikipedia.org /wiki/Rank_of_an_abelian_group (665 words)

	Torsion (Site not responding. Last check: 2007-10-08)
		A second meaning of torsion in differential geometry is the torsion tensor, which depends on a connection.
		Torsion free connections are considered most frequently - the Levi-Civita connection is assumed to have zero torsion, for instance.
		Torsion is also sometimes used for the medical condition commonly known as bloat.
	www.sciencedaily.com /encyclopedia/torsion (318 words)

	Torsion free (Site not responding. Last check: 2007-10-08)
		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.
		Even if G is not finitely generated, the size of its torsion free part is uniquely determined, as isexplained in more detail in the article on rank of anabelian group.
		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 mapbetween the tensor products K ⊗ G andH ⊗ G is injective.
	www.therfcc.org /torsion-free-355403.html (531 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Corollary.} {Over a PID a finitely generated module $_RM$ is torsion free iff it is free.} {\bf Proof.} We may assume that $M\not= 0$ is torsion free.
		Therefore, since $a\not= 0$ and $M$ is torsion free, the map $\lambda_a:x\longmapsto ax$ is a monomorphism $\lambda_a:M\longrightarrow F$.
		And for that we may assume that $M$ is torsion and then induct on the number of primes that appear as factors of the elementary divisors of $M$.
	darkwing.uoregon.edu /~anderson/math648/lecture12.html (1662 words)

	RMK articles : Chirality and Helicity vs Topological Spin and Topological Torsion (Site not responding. Last check: 2007-10-08)
		From a topological viewpoint, Maxwell's electrodynamics indicates that the concept of Chirality is to be associated with a third rank tensor density of Topological Spin induced by the interaction of the 4 vector potentials {A, phi } and the field excitations (D, H).
		The distinct concept of Helicity is to be associated with the third rank tensor field of Topological Torsion induced by the interaction of the 4 vector potentials and field intensities (E, B).
		The 4-divergence of the topological Torsion is equal to the second Poincare Invariant.
	www22.pair.com /csdc/pd2/pd2fre52.htm (462 words)

	BACKGROUND
		An outer automorphism $\Phi$ of a free group $F$ of finite rank is said to be reducible if there is a free factorization $F=F\sb 1 \star \cdots\star F\sb k\star F'$ such that $\Phi$ permutes the conjugacy classes of the subgroups $F\sb 1,\cdots,F\sb k$; otherwise, $\Phi$ is irreducible.
		Then the automorphism of the free group F that takes x_1 to x_1 x_2^m and fixes all other generators, is identical on R, but is not inner.
		It is known that the first part of this algorithm (reducing a given free word to a free word of minimal possible length by "elementary" Whitehead automorphisms) is pretty fast (of quadratic time with respect to the length of the word).
	www.cs.gc.cuny.edu /~cryptlab/gworld/problems/Back.html (5364 words)

	Lee Lady: Finite Rank Torsion Free Modules over Dedekind Domains (a book)
		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.
		And one becomes more aware of the fact that the theory of finite rank torsion free abelian groups is moving away from abelian group theory in general in much the same fashion that abelian group theory has moved away from general group 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)

	Talk:Torsion - Wikipedia, the free encyclopedia
		It may be a fine link to a paper in Gauge Theory of Gravity (or not, I didn't check, and I'm not sure whether I'm fit to judge), but it obviously doesn't clarify Torsion as mathematical concept.
		I am quite sure that torsion is T = ((r` x r``) * r```) / ((r` x r``)^2) So the denominator is square.
		I guess it's also a strong argument against math tex mode, templates and similar gimmicks: they significantly increase the hurdle to contribute and fix stuff on the spot.
	www.wikipedia.org /wiki/Talk:Torsion (233 words)

	Suspension support structure being free from torsion and pinch - Patent 4779855 (Site not responding. Last check: 2007-10-08)
		However, torsion and pinch such as to deform both elastic bodies about an axis of a piston rod act on both elastic bodies through spring reaction transmitted to the spring seat in bound and rebound of a wheel.
		Since no torsion and pinch are found in the elastic body of the first support means, the spring property of the elastic body is not changed and the characteristics of the vehicle may be held at a set condition.
		The bushing 55a of the second support means 54 is adhered on an outer peripheral surface thereof to the mounting portion 21a of the spring seat 22 and on an inner peripheral surface thereof to the inner tube 55c respectively.
	www.freepatentsonline.com /4779855.html (2358 words)

	[No title]
		whose torsion subgroup is the direct _sum_ of the cyclic factors.
		The torsion subgroup is in turn a direct sum of its p-primary subgroups.
		It is similarly true that one can make some headway characterizing Abelian groups with some other limiting condition, such as divisible groups, groups of bounded height, matrix groups, etc. Of course there's more to do in a field than simply find a structure theorem for the objects.
	www.math.niu.edu /~rusin/known-math/99/ab_gps (613 words)

	Torsion (Site not responding. Last check: 2007-10-08)
		In the elementary differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting.
		The torsion of a curve will be zero if and only if the curve sits inside a fixed plane.
		Torsion fields are infamous as a pseudoscientific field popular in Russia.
	www.worldhistory.com /wiki/T/Torsion.htm (426 words)

	Bibliography for Torsion Free Groups (Site not responding. Last check: 2007-10-08)
		M.C.R. Butler, A class of torsion free groups of finite rank, Proc.
		Murley, The classification of certain classes of torsion free abelian groups, Pac.
		Arnold, A duality for torsion free modules of finite rank over a discrete valuation ring, Proc.
	www.math.hawaii.edu /~lee/book/ref.html (367 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		While the interactions of both graviton and torsion in the bulk are controlled by the Planck mass, an additional exponential suppression comes for the torsion zero-mode on the visible brane.
		This may serve as a natural explanation of why the effect of torsion is so much weaker than that of curvature on the brane.
		The massive torsion modes, on the other hand, are correlated with the corresponding gravitonic modes and may be detectable in TeV-scale experiments.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20443379 (255 words)

	[No title]
		It must be torsion free, but the example of G/T = additive group of the rationals shows that it need not be.
		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.
		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)

	Torsion
		Given a vector-valued function r(t), the torsion at a given value of t is
		In the Tor functors of homological algebra, which arise because tensor product doesn't in general preserve exact sequences, the symbol Tor does stand for this kind of algebraic torsion, historically speaking anyway.
		All text is available under the terms of the GNU Free Documentation License.
	news-server.org /t/to/torsion.html (240 words)

	Moduli spaces for torsion free modules on curve singularities I - Greuel, Pfister (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: this article is to construct coarse moduli spaces for torsion free R-modules or, which amounts to the same, for Cohen-Macaulay representations of R. (Update)
		in the local case of torsion free modules on curve singularities.
		Greuel, G.-M.; Pfister, G.: Moduli spaces for torsion free modules on curve singularities.
	citeseer.ist.psu.edu /greuel93moduli.html (437 words)

	[No title]
		It is an interesting problem to consider which infinite loop s* paces have 2-torsion free* homology, and what limits that assumption puts on the torsi* *on in homotopy.
		Though the vector spaces M+ and M- are not closed under the action of the full Steenrod algebra, the condition that H(X; Z(p)) is torsion* free can be combined with the Nishida relations to show that M+ and M- are closed under the action of the subalgebra generated by the reduced power operations.
		The bulk of the work occurs in the proof of Proposition 3.1, which shows that a certain sub-Hopf algebra of the mod p cohomology of X is a free commutative algebra.
	hopf.math.purdue.edu /Slack/tfodd.txt (2262 words)

	adidas Women's Torsion Open Shoe - Free Shipping
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	DC MetaData pour: The group of fractions of a torsion free lcm monoid is torsion free (Site not responding. Last check: 2007-10-08)
		DC MetaData pour: The group of fractions of a torsion free lcm monoid is torsion free
		The group of fractions of a torsion free lcm monoid is torsion free
		Inparticular, the fact that Artin braid groups are torsion free now follows from Garside\'s results almost immediately.
	math-sahel.ujf-grenoble.fr /prepub-ccsd/ccsd-00000852.html (88 words)

	Finitely Generated and Torsion Free is Free (Site not responding. Last check: 2007-10-08)
		Let r be a pid and let m be a torsion free r module.
		Because m is torsion free, the kernel of this homomorphism is 0.
		Note, Q is an infinitely generated torsion free Z module that is not free.
	www.mathreference.com /mod-pid,fgtf.html (216 words)

	torsion (Site not responding. Last check: 2007-10-08)
		In this case the torsion would not be zero.
		In some other theories of gravity there is torsion.
		But there's no experimental evidence for torsion, so most people stick with GR.
	math.ucr.edu /home/baez/gr/torsion.html (413 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Then K is a finitely generated free module which can be generated by n elements or less.
		Then F is a free submodule of M. Let m be an element of M. Suppose that the image of m in N is r1n1++rtnt.
		Since a free module is torsion-free, the intersection of F and Mtor is 0.
	www.math.ucla.edu /~blasius/110bh.1.01w/modulesoverpids.doc (1101 words)

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	DC MetaData for: Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
		We obtain an expression for the Reidemeister torsion of the mapping torus of the dual
		This means that the Reidemeister torsion counts the fixed point classes of all iterates
		In section 6.3 we establish a connection between the Reidemeister torsion of a mapping torus,
	www.esi.ac.at /Preprint-shadows/esi539.html (610 words)

	Torsion - index page - Free MP3 downloads, CDs, Bio Info, Tour Dates, Lyrics and More!" (Site not responding. Last check: 2007-10-08)
		Torsion is a four piece Rock / Industrial band based out of the Philadelphia Suburbs.
		Then you will be up to date on all Torsion shows and news.
		To buy Torsion’s latest CD, send a request to the e-mail address, and we can arrange shipment.
	artists.iuma.com /IUMA/Bands/Torsion (134 words)

	Torsion, Order Ideal (Site not responding. Last check: 2007-10-08)
		A module is torsion free if it has no torsion elements, and torsion if it equals its torsion submodule.
		If h(c) is torsion then c maps into the kernel, which is torsion, hence c is torsion.
		It is zero iff c is torsion free.
	www.mathreference.com /mod-pid,torord.html (333 words)

	Army Technology - DOLL - Military Platform Bodies, Semitrailers, Vehicle-Mounted Antenna Systems and Other Military ...
		In addition to vehicle-mounted antenna mast systems, torsion-free platform bodies and low-bed and drop-bed semitrailers, DOLL produces mobile supply and workshop shelters, chassis for field kitchens, system frames for the missile launchers, system frames for radar control, recovery jigs for aircraft and container chassis.
		DOLL's torsion-free platform body is fixed on an auxiliary frame by three-point bedding allowing the flat bed to maintain a horizontal position at all times by keeping the body structure independent of the torsion of the truck chassis.
		The platform has a length of between 5m and 8m and is equipped with easily replaceable locking systems, dropsides and taillifts.
	www.army-technology.com /contractors/vehicles/doll (479 words)

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