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Topic: Archimedean group

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	PlanetMath: proof of embedding theorem for ordered abelian groups of rank one (Site not responding. Last check: 2007-10-08)
		Since the real numbers enjoy the Archimedean property and it is obvious that any subset of a set enjoyying the Archimedean property also enjoys this property, it follows that every subgroup of the additive group of the real numbers enjoys the Archimedean property.
		It only remains to show that every group enjoying this property is isomorphic to a subgroup of additive group of the real numbers.
		This is version 18 of proof of embedding theorem for ordered abelian groups of rank one, born on 2005-01-03, modified 2005-01-04.
	planetmath.org /encyclopedia/ProofOfTheoremAboutRankOneAbleianGroups.html (616 words)

	Archimedean group -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In (additional info and facts about abstract algebra) abstract algebra, a branch of (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, an Archimedean group is an (additional info and facts about algebraic structure) algebraic structure.
		We can also say that an Archimedean group is a (additional info and facts about linearly ordered group) linearly ordered group for which the (additional info and facts about Archimedean property) Archimedean property holds.
		In the subsequent, we use the notation (where is in the set N of (The number 1 and any other number obtained by adding 1 to it repeatedly) natural numbers) for the sum of a with itself n times.
	www.absoluteastronomy.com /encyclopedia/a/ar/archimedean_group.htm (309 words)

	Archimedean group - Wikipedia, the free encyclopedia
		In abstract algebra, a branch of mathematics, an Archimedean group is an algebraic structure.
		We can also say that an Archimedean group is a linearly ordered group for which the Archimedean property holds.
		In the subsequent, we use the notation na (where n is in the set N of natural numbers) for the sum of a with itself n times.
	en.wikipedia.org /wiki/Archimedean_group (282 words)

	Archimedean property - Wikipedia, the free encyclopedia
		In mathematics, the Archimedean property of an ordered algebraic structure, such as a linearly ordered group, and in particular of the real numbers, is the property of having no (non-zero) infinitesimals.
		Structures that lack infinitesimals are called Archimedean; those that possess infinitesimals are non-Archimedean.
		A small number x is classed as infinitesimal if the inequality
	en.wikipedia.org /wiki/Archimedean_property (265 words)

	AMCA: Epi-topology on an archimedean l-group with unit by Anthony W. Hager (Site not responding. Last check: 2007-10-08)
		AMCA: Epi-topology on an archimedean l-group with unit by Anthony W. Hager
		W is the category of archimedean l-groups with distinguished weak unit, with unit-preserving l-homomorphisms.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/m/j/18.htm (97 words)

	Archimedean Semi-Regular Polyhedra
		All but one of these polyhedra were gradually rediscovered during the Renaissance by various artists, and Kepler finally reconstructed the entire set in 1619.
		A key characteristic of the Archimedean solids is that each face is a regular polygon, and around every vertex, the same polygons appear in the same sequence, e.g., hexagon-hexagon-triangle in the truncated tetrahedron, shown above.
		The Archimedean solid (shown at right) in which three squares and a triangle meet at each vertex is the rhombicuboctahedron.
	www.georgehart.com /virtual-polyhedra/archimedean-info.html (628 words)

	[No title]
		The summand-inducing hull of an Archimedean $l$-group with unit.
		Proceedings of the Conference on Lattice-Ordered Groups and $f$-Rings held at the University of Florida, Gainesville, FL, February 28--March 3, 2001.
		The hyper-archimedean kernel sequence of a lattice-ordered group.
	www.math.ufl.edu /fac/facmr/Martinez.html (481 words)

	Abstract
		We speculate that he must have been delighted to find that permutation groups determined by the Platonic solids define all the groups so associated.
		Figure 11, we see that Maschke associated the dihedral groups with the rotations of a dihedron (a solid determined by a regular n-gon on the equator of a sphere, with an additional vertex at each pole).
		Figure 2, for the dihedral group determined by the triangle in this case, is easily explained in terms of a cyclic element of order n and any reflection.
	www.lcsc.edu /csteenbe/abstract.htm (3076 words)

	Weekly Calendar (Site not responding. Last check: 2007-10-08)
		The classical unanswered question in the theory of totally ordered groups (o-groups) is whether or not every o-group can be embedded in a divisible o-group.
		Holland proved in 1961 the existence of an example of an o-group of archimedean rank 3 that is not embeddable in a divisible o-group of achimedean rank 3.
		G can be embedded in an o-group of archimedean rank at most 2n where a has a square root.
	www-math.bgsu.edu /oldcalendars/2002-02-25.html (249 words)

	The Geometry Junkyard: Symmetry and Group Theory
		Convex Archimedean polychoremata, 4-dimensional analogues of the semiregular solids, described by Coxeter-Dynkin diagrams representing their symmetry groups.
		Jonathan A. Poritz and coworkers investigate the fundamental domains of cyclic group actions on hyperbolic 3-space, resulting in lots of pretty pictures of overlapping spheres.
		Group theoretic mathematics for determining whether a polygon formed out of hexagons can be dissected into three-hexagon triangles, or whether a polygon formed out of squares can be dissected into restricted-orientation triominoes.
	www.ics.uci.edu /~eppstein/junkyard/sym.html (1155 words)

	TOPCOM, Michael R. Darnel: Theory of Lattice-Ordered Groups; a review of the book and perspective of the literature by ...
		It was the first of its kind to lace together the Conrad opus on lattice-ordered groups with contributions from others (Simon Bernau, most prominently) who approached the subject matter from the analytic point of view, and brought to the game elements of topology, for purposes of representation.
		By the end of the seventies then many of us involved with lattice-ordered groups began to see the need for another monograph, and, indeed, as [BKW77] was so long in gestation, it was also out of date when it appeared, and addressed the subject of ordered permutation groups only glancingly.
		The reader who is familiar with varieties of groups might recall that a similar theorem holds for varieties in that context.
	at.yorku.ca /t/o/p/c/39.htm (3409 words)

	Platonic polyhedra (Site not responding. Last check: 2007-10-08)
		View the archimedean polyhedra from the tetrahedron family.
		View the archimedean polyhedra from the cube/octahedron family.
		View the archimedean polyhedra from the dodecahedron/icosahedron family.
	www.phys.uu.nl /~beugelng/polyhedra/platonics.html (135 words)

	Functorial Rings of Quotients, III: the Maximum in Archimedean f-Rings - Hager, Martinez (ResearchIndex)
		Abstract: The category of discourse is Arf, consisting of archimedean f-rings with identity and `-homomorphisms which preserve the identity.
		3 The hulls of representable `{groups and f{rings (context) - Conrad - 1973
		1 The additive group of an f{ring (context) - Conrad - 1974
	citeseer.ist.psu.edu /474107.html (607 words)

	Articles - Algebraic structure (Site not responding. Last check: 2007-10-08)
		For example, a topological group is a topological space with a group structure such that the operations of multiplication and taking inverses are continuous; a topological group has both a topological and an algebraic structure.
		This category, being a concrete category, may be regarded as a category of sets with extra structure in the category-theoretic sense.
		Similarly, the category of topological groups (with continuous group homomorphisms as morphisms) is a category of topological spaces with extra structure.
	www.lastring.com /articles/Algebraic_structure?mySession=212cf973f817176716c66f3d09ad7c9c (611 words)

	Functorial Approximations To The Lateral Completion In Archimedean (ResearchIndex)
		8 Algebraic extensions of an archimedean lattice-ordered group..
		1 Epicompletions of archimedean lattice-ordered groups (context) - Kizanis - 1991 ACM
		1 the structure of a class of archimedean lattice-ordered alge..
	citeseer.ist.psu.edu /616303.html (645 words)

	Profile
		My training and dissertation, written under the direction of W. Holland, were in l-permutation groups.
		This completion is a sublattice of the essential hull of a given l-group in the category of distributive lattices; it contains virtually all known completions of interest.
		Ball, R.N., Distinguished extensions of a lattice-ordered group, Alg.
	myprofile.cos.com /rball (470 words)

	Vignettes on automorphic and modular forms, representations, L-functions, and number theory
		We want to prove that the singular homology of quotients X/Gamma is the group homology of Gamma, under some mild conditions on X (such as that X be a ball).
		Recollection of some basic facts on discrete series of real reductive groups, with table showing which classical groups do and don't have discrete series, holomorphic discrete series, and quaternionic discrete series.
		Standard basic features of representation theory of p-adic reductive groups: exactness of Jacquet module functors, Jacquet's lemmas, admissibility and finite-generation of Jacquet modules of admissible finitely-generated smooth representations.
	www.math.umn.edu /~garrett/m/v (1093 words)

	Bibliography for Buildings and Classical Groups
		C.W. Curtis, The Hecke algebra of a finite Coxeter group, Arcata Congerence on Representations of Finite Groups, pp.
		Kostant, On convexity, the Weyl group, and the Iwasawa decomposition, Ann.
		A.V. Zelevinsky, Induced represenatations of reductive p-adic groups II: On irreducible representations of GL(n), Ann.
	www.math.umn.edu /~garrett/m/buildings/biblio.html (3202 words)

	Dan Ciubotaru - Research Interests
		A fundamental problem, motivated by the applications to harmonic analysis and number theory, is the classification of the unitary representations.
		was determined by Vogan (archimedean case) and Tadic (nonarchimedean).
		There are some other particular cases in which the unitary dual is known, but in general, this is very much an open problem.
	www.math.cornell.edu /~ciubo/res.html (269 words)

	Four Dimensional Figures Page
		You should be fairly well acquainted with the convex uniform polyhedra and their symmetry groups, and somewhat well acquainted with the six convex regular polytopes in four-dimensional space and their symmetry groups, if the following material is to make any sense to you.
		Below are tabulated the six Archimedean prisms and antiprisms that occur as cells of the nonprismatic convex Archimeadean polychora.
		Likewise, all the vertices of an n-dimensional uniform polytope are constrained by symmetry to lie on a single n-dimensional sphere centered at the polytope’s center of symmetry.
	members.aol.com /Polycell/uniform.html (4231 words)

	PlanetMath: (Site not responding. Last check: 2007-10-08)
		decomposable group (in indecomposable group) owned by smw
		decomposition and inertia group for archimedean places (in ramification of archimedean places) owned by alozano
		dimension of the special orthogonal group owned by stevecheng
	planetmath.org /encyclopedia/D (1510 words)

	More On The Laterally sigma-Complete Reflection Of An Archimedean Lattice-Ordered Group (ResearchIndex)
		5 groups and vector lattices with weak unit (context) - Ball, Hager et al.
		2 groups and vector lattices (context) - Ball, Hager et al.
		Hulls For Various Kinds Of alpha-Completeness In Archimedean..
	citeseer.ist.psu.edu /469130.html (414 words)

	Atlas: o-Automorphisms of o-Groups of Finite Rank by Ramiro H. Lafuente-Rodriguez (Site not responding. Last check: 2007-10-08)
		A group G is divisible if for every g in G and every natural number n, there exists x in G such that x
		W.C.Holland proved in 1961 the existence of an example of an o-group of archimedean rank 3 that is not embeddable in a divisible o-group of archimedean rank 3.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cain-13.
	atlas-conferences.com /cgi-bin/abstract/cain-13 (220 words)

	The Geometry Junkyard: Spirals
		Archimedean spiral extended into three dimensions, from the Mathematica graphics gallery.
		Ford circles and circle inversions, Kleinian groups, more Kleinian groups, even more Kleinian groups, 3d sphere packings, spiral circle packings, and sphere inversion fractals.
		Bo Atkinson studies the geometry of a solid of revolution of an Archimedean spiral.
	www.ics.uci.edu /~eppstein/junkyard/spiral.html (508 words)

	Abstract (Site not responding. Last check: 2007-10-08)
		In this paper we consider group actions on generalised treelike structures (termed ``pretrees'') defined simply in terms of betweenness relations.
		Using a result of Levitt, we show that if a countable group admits an archimedean action on a median pretree, then it admits an action by isometries on an $ {\Bbb R} $-tree.
		Thus the theory of isometric actions on $ {\Bbb R} $-trees may be extended to a more general setting where it merges naturally with the theory of right-orderable groups.
	www.maths.soton.ac.uk /~bhb/abstracts/arc.html (106 words)

	Science Museum Math Exhibit
		This is an especially difficult task at a museum; the average length of stay at the exhibit is only about five minutes.
		Reflections across the edges of the base triangle are the generators of the group.
		In the language of group theory, the vertices are images of the bending point under the action of the group.
	www.geom.uiuc.edu /docs/forum/museum/museum.html (810 words)

	Atlas: Propaganda for Polar Functions by Jorge Martinez (Site not responding. Last check: 2007-10-08)
		A polar function is an assignment of an archimedean l-group with weak unit G to a sublattice X(G) of the algebra of polars.
		They are models for some rather natural constructions in archimedean l-groups.
		And they have a nice associated "dual"; namely the notion of a covering function: an assignment which assigns a compact space X to a subalgebra K(X) of the algebra of regular closed sets.
	atlas-conferences.com /cgi-bin/abstract/cain-02 (136 words)

	Papers by Robert Benedetto
		A wavelet theory is developed on G using coset representatives of the discrete quotient of the dual of G by the annihilator of H to circumvent this limitation.
		Although the Haar and Shannon wavelets are naturally antipodal in the Euclidean setting, it is observed that their analogues for G are equivalent.
		Abstract: Let G be a locally compact abelian group with a compact open subgroup H.
	www.cs.amherst.edu /~rlb/papers (1226 words)

	Catalogue of GP/PARI Functions: Functions related to general number fields
		Buchmann's sub-exponential algorithm for computing the class group, the regulator and a system of fundamental units of the general algebraic number field K defined by the irreducible polynomial P with integer coefficients.
		In this case, the corresponding congruence group is a product of cyclic groups and, for the time being, the class field has to be obtained by splitting this group into its cyclic components.
		The algorithm looks for a solution x which is an S-integer, with S a list of places of K containing at least the ramified primes, the generators of the class group of L, as well as those primes dividing a.
	megrez.math.u-bordeaux.fr /dochtml/html.stable/Functions_related_to_general_number_fields.html (12903 words)

	Choice and Constraint
		This analysis is optimistic, for it suggest that unless a catastrophe damages us enough or a powerful government stops or slows change, for example, by hindering innovation, democracy will survive.
		The political implication of this exercise is that wise anti-trust actions against both monopoly and oligopoly are required even when there are few or no `barriers to entry'.
		The last grouping is a catchall for those not in the first two groups.
	www.rattlesnake.com /notions/put-together-1.html (19350 words)

	WEAK UNITS IN EPICOMPLETIONS OF ARCHIMEDEAN LATTICE-ORDERED GROUPS (Site not responding. Last check: 2007-10-08)
		WEAK UNITS IN EPICOMPLETIONS OF ARCHIMEDEAN LATTICE-ORDERED GROUPS
		In [14] it is shown that in the category of archimedean lattice-ordered groups with
		Since, in general, these epicomplete objects have no concrete realization and since epicomplete objects in the category of archimedean lattice-ordered groups with distinguished weak order unit and unit preserving
	math.la.asu.edu /~rmmc/rmj/VOL30-4/KIZ/KIZ.html (97 words)

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