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Topic: Stabilizer subgroup

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	General linear group - Wikipedia, the free encyclopedia
		These groups are important in the theory of group representations, and also arise in the study of spatial symmetries and symmetries of vector spaces in general, as well as the study of polynomials.
		The maximal compact subgroup of GL(n, R) is the orthogonal group O(n), while the maximal compact subgroup of GL n, R) is the special orthogonal group SO(n).
		This requires only finding the order of the stabilizer subgroup of one (described on that page in block matrix form), and divide into the formula just given, by the orbit-stabilizer theorem.
	en.wikipedia.org /wiki/General_linear_group (1142 words)

	Sylow theorem - Wikipedia, the free encyclopedia
		Let p be a prime number; then we define a Sylow p-subgroup of G to be a maximal p-subgroup of G (i.e., a subgroup which is a p-group, and which is not a proper subgroup of any other p-subgroup of G).
		Collections of subgroups which are each maximal in one sense or another are not uncommon in group theory.
		The problem of finding a Sylow subgroup of a given group is an important problem in computational group theory.
	en.wikipedia.org /wiki/Sylow_theorem (1070 words)

	PlanetMath: conjugate stabilizer subgroups
		Thus all stabilizer subgroups for elements of the orbit
		"conjugate stabilizer subgroups" is owned by Thomas Heye.
		This is version 4 of conjugate stabilizer subgroups, born on 2003-01-07, modified 2003-02-12.
	planetmath.org /encyclopedia/ConjugateStabilizerSubgroups.html (49 words)

	Invariants
		This group is 2-transitive and the stabilizer of two points is transitive on those points that lie in the same image of the determinant, that is those that are either all squares or all non-squares.
		The stabilizer will be trivial in the case where we know in advance that already the stabilizers of all 5-sets are trivial.
		or 140 orbits with trivial stabilizer for a
	www.mathe2.uni-bayreuth.de /discreta/ONLINE/boca2002/node4.html (1886 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		This construction is complemented by a verify-routine that either proves the correctness of the stabilizer chain or causes the extension of the chain to a correct one.
		This means that a membership test with this stabilizer chain returns `false' for all elements that are not in $G$, but it may also return `false' for some elements of $G$; in other words, the result `true' of a membership test is always correct, whereas the result `false' may be incorrect.
		`stabilizer' & If the current stabilizer is not yet the trivial group, the stabilizer chain continues with the stabilizer of the current base point, which is again represented as a record with components `labels', `identity', `genlabels', `generators', `orbit', `translabels', `transversal' (and possibly `stabilizer').
	www-groups.dcs.st-and.ac.uk /gap/Manuals/doc/build/grpperm.msk (3012 words)

	Stabilizers of Vertices and Edges (Site not responding. Last check: 2007-10-16)
		The stabilizer of the sequence of vertices Q of the graph G in the subgroup A of Aut(G).
		The stabilizer of the edge e of the graph G in the subgroup A of Aut(G).
		The stabilizer of the sequence of edges R of the graph G in the subgroup A of Aut(G).
	www.math.uiuc.edu /Software/magma/text465.html (124 words)

	GAP Manual: 21 Permutation Groups
		Otherwise a stabilizer chain with the lexicographically smallest reduced base is computed and the indices corresponding to this chain are returned (see Stabilizer Chains).
		The image of a subgroup, the preimage of an element, and the preimage of a subgroup are computed by rather complicated algorithms.
		The reason is mainly the creation of stabilizer chains (see StabChain): During this process a lot of schreier generators are produced for the next point stabilizer in the chain, and these generators must be processed.
	parallel.rz.uni-mannheim.de /gap/htm/CHAP021.htm (4672 words)

	Lifting a McL quotient
		of a subgroup is not necessarily the action on the cosets, but only some homomorphism whose kernel is contained in the subgroup.
		However creating a stabilizer chain for a permutation group of this size is very memory consuming.
		This stabilizer chain calculation is by far the hardest part of the whole calculation and can take a few hours.
	www.math.colostate.edu /~hulpke/paper/quot_gap.html (1347 words)

	[No title]
		Mono(SU (3; 3); F4) is transitive and the stabilizer subgroup at the centric monomorphism e, i.e.
		Since the two stabilizer subgroups W (F4)A(2;1)and W (F4)A(0;1)are* * conjugate in W (F4), the two maximal torus normalizers are isomorphic and hence the two centralizers* * are isomorphic, too, by N-determinism [15] [19].
		-invariant subgroup of the homot* *opy of BSU (3).
	hopf.math.purdue.edu /Moller/toricrep.txt (9877 words)

	Group action -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-16)
		If we define N =, then N is a (additional info and facts about normal subgroup) normal subgroup of G; indeed, it is the kernel of the homomorphism G → Sym(G).
		This is a ((mathematics) a subset (that is not empty) of a mathematical group) subgroup of G, though typically not a normal one.
		Every transitive G action is isomorphic to left multiplication by G on the set of left (additional info and facts about coset) cosets of some ((mathematics) a subset (that is not empty) of a mathematical group) subgroup H of G.
	www.absoluteastronomy.com /encyclopedia/g/gr/group_action.htm (1813 words)

	p Cycles and Normal Subgroups (Site not responding. Last check: 2007-10-16)
		Let h be the subgroup of g that maps the block t onto itself.
		Suppose the stabilizer of x, call it j, is contained in a larger subgroup h.
		Assume g is primitive on n letters, j is the stabilizer of x, and k is a normal subgroup of g.
	www.mathreference.com /grp-fin,nsubpg.html (520 words)

	Subgroups of order up to 6 in
		there are the following stabilizers and the corresponding numbers of orbits of 6-sets.
		There is just one orbit with this stabilizer on 6-sets.
		So, they are stabilizers of 6-sets from different orbits.
	www.mathe2.uni-bayreuth.de /discreta/ONLINE/boca2002/node3.html (464 words)

	GAP Manual: 25 Finite Polycyclic Groups
		The following sections describe how subgroups of ag groups are represented (see More about Ag Groups), additional operators and record components of ag groups (see Ag Group Operations and Ag Group Records) and functions which work only with ag groups (see Ag Group Functions and Subgroups and Properties of Ag Groups).
		We call G a parent, that is a ag group with collector and U a subgroup, that is a group which is obtained as subgroup of a parent group.
		Subgroup functions which work for various types of groups are described in Subgroups.
	www.math.jussieu.fr /~jmichel/htm/CHAP025.htm (8026 words)

	Bulding Stabilizer Chains
		Creates a table of elements that generate a stabilizing subgroup of G
		This Table has two fields: one which is a Table containing the generators of a stabilizer Subgroup and another one which is an image of the previous, bur rather than storing the generators as permutation cycles, it has them as words of Abstract Generators of the original group G
		Creates the left Schreier transversal in G of a stabilizer subgroup with respect to the base base
	www.csi.uottawa.ca /~istvan/rubik/apps/algebra/stabilizer.html (272 words)

	Re: Symmetry and Information
		Fortunately, all we need do in order to verify this is to check that H really is the stabilizer of a particular point in S^n in the action by G on S^n and likewise K for a particular point in RP^n.
		Here the fact that SO(n+1,R) is a subgroup of index two of O(n+1,R) hints at an important theme in Kleinian geometry: -larger- groups G correspond to -less rigid- geometries G/H. (4) This distinction between proper and improper transformations is probably easier to understand in a setting with which everyone is familiar: "high school geometry".
		This gives the same Lie algebra as before, but this time the stabilizer H of the origin is group isomorphic to SO(n,R).
	www.lns.cornell.edu /spr/2002-04/msg0040885.html (1609 words)

	The Automorphism Group of an Incidence Structure
		The image of the sequence Q of blocks of the incidence structure D under the action of the subgroup B of the automorphism group of D (returns a set of sequences of blocks).
		The image of the block b of incidence structure D under the action of the subgroup B of the automorphism group of D (returns a set of blocks).
		Given an incidence structure D on a set of n points and a subgroup A of Sym(n), construct the orbit of the incidence structure D under A (returns a set of incidence structures).
	www.math.ufl.edu /help/magma/text507.html (924 words)

	[No title]
		Since T is a characteristic subgroup of N = ToW, there is an exact sequence 1 -!AutW (T) -!Aut(N) -!Aut(W); where AutW (T) denotes the group of W -equivariant automorphisms of T, and an * exact sequence T) Aut(N) 1 -!Aut_W(__Z(W-)!____W-!Out(W) obtained by quotienting out the normal subgroup* W / Aut(N).
		For instance, the subgroup S3 (P 3) of GL(2; F3) is the Weyl group o* *f the 3-compact group SU(3) (PU (3)).
		G2arising in the construct* *ion (4.1) of BG2 as a homotopy colimit is N-determined and centric.
	hopf.math.purdue.edu /Moller/di2.txt (4341 words)

	thesis71
		The purpose of the present paper is to initiate the study of the possibility of finding explicit representations of the Poincaré group, which are labeled by additional discrete quantum numbers.
		It is immediately obvious, however, that to include quantum numbers such as those associated with isospin, a space is needed which is itself larger than the Poincaré group due to the circumstance that the maximal compact subgroup has already been pressed into service to carry the spin spectrum.
		the abelian subgroup A is a three-parameter group, the nilpotent subgroup N is a six-parameter group.
	www.draken.com /drakenr/Paper01.htm (3845 words)

	VEGA 0.5 Quick Reference Manual: Functions in GROUPS.M
		LeftCoset[g,H,op] finds the left coset gH of the group element g for the subgroup H and the group operation op.
		among the orbits of the stabilizer of the m-th element of the
		SubgroupAction[genG,genH,op] constructs a group action of the group H with the group operation op, generated by genH on the left cosets of the group G, generated by genG, in which H is a subgroup.
	vega.ijp.si /Htmldoc/usages/GROUPS.HTM (1853 words)

	GAP Manual: 60.22 WyckoffLattice (Site not responding. Last check: 2007-10-16)
		If a point x in a Wyckoff position W_1 has a stabilizer which is a subgroup of the stabilizer of some point y in a Wyckoff position W_2, then the closure of W_1 will contain W_2.
		Number of Wyckoff positions having a stabilizer whose point group is in the same subgroup conjugacy class.
		Prints (in the GAP window) information about each of the conjugacy classes of the stabilizer, namely the order, the trace and the determinant of its elements, and the size of the conjugacy class.
	www-gap.dcs.st-and.ac.uk /Gap3/Manual3/C060S022.htm (258 words)

	IDA: Interactive Document on Algebra
		4.3, Proposition: characterization of a subgroup generated by a subset of a group
		6.3, Proposition: the kernel of a morphism is a normal subgroup
		2.3, Theorem: a transitive representation is equivalent to left multiplication on cosets of stabilizer
	www.win.tue.nl /ida/demo/indextb.html (934 words)

	Projective Geometry I - Lecture Notes (Site not responding. Last check: 2007-10-16)
		Example: Aut C is a subgroup of Perm C, where C is a configuration (identified with its points).
		Lemma 4.11: Let H be a subgroup of G, and let gH be a left coset.
		Def: If G is a subgroup of some Perm S, the orbit of x.
	www-math.cudenver.edu /~wcherowi/courses/m6221/pglc4.html (217 words)

	A Survey of Distance-Transitive Graphs
		G has an elementary abelian normal subgroup which is regular on V.
		is the stabilizer in G of 0 in V.
		V is 1-dimensional and H is a subgroup of GamL(1,s);
	www.win.tue.nl /~amc/oz/dtg/survey.html (785 words)

	PlanetMath: flag variety (Site not responding. Last check: 2007-10-16)
		, and the stabilizer of a point is a parabolic subgroup.
		In particular, the complete flag variety is isomorphic to
		Cross-references: Borel subgroup, isomorphic, homogeneous space, parabolic subgroup, stabilizer, group, projective variety, closed, image, natural embedding, flags, sequence, dimension, vector space, field
	www.planetmath.org /encyclopedia/FlagManifold.html (101 words)

	[ref] 41 Permutation Groups
		interactively, one might be able to choose subgroups of small index for which the cores intersect trivially; in this case, the actions on the cosets of these subgroups give rise to an intransitive permutation representation the degree of which may be smaller than the original degree.
		Before we describe the construction of stablizer chains in Construction of Stabilizer Chains, we explain in Randomized Methods for Permutation Groups the idea of using non-deterministic algorithms; this is necessary for understanding the options available for the construction of stabilizer chains.
		If the current stabilizer is not yet the trivial group, the stabilizer chain continues with the stabilizer of the current base point, which is again represented as a record with components
	wwwmaths.anu.edu.au /research.programs/aat/GAP_manual/ref/CHAP041.htm (4293 words)

	Re: Decomposing Lie Groups (Site not responding. Last check: 2007-10-16)
		In my understanding, symmetry is broken down to a subgroup, not a subgroup and something else.
		If there is a particular state in your theory that breaks the symmetry, you have to determine the stabilizer subgroup of that state.
		From what I've seen of analysis of broken symmetry, your next step should be to take whatever linear representations of the original group occur in your theory and decompose them into direct sums of representations of the residual symmetry subgroup.
	www.lns.cornell.edu /spr/2005-02/msg0067112.html (171 words)

	Classes previously taught by Alexander Yong (Site not responding. Last check: 2007-10-16)
		Cyclic groups, any subgroup of a cyclic group is cyclic (idea of proof: in the end, consider the division algorithm).
		Centers, commutator subgroups, we care since they give measures of how abelian a group is. Understanding groups, by moding out by e.g., commutator subgroups, group actions, example of group actions, actions of groups on themselves by left multiplication, conjugation.
		The kernel of Phi is Stab_{G}(X), the stabilizer subgroup of X. This kernel is {e} iff Phi is 1-1 iff Stab_{G}(X)={e} iff G's action on X is "faithful".
	math.berkeley.edu /~ayong/old_teaching.html (3007 words)

	GAP Manual: 21 Permutation Groups
		The chain of subgroups of G itself is called the stabilizer chain of G relative to B.
		Otherwise a stabilizer chain with the lexicographically smallest reduced base is computed and a strong generating set corresponding to this chain is returned (see Stabilizer Chains).
		If it is set to a number i between 1 and 1000 at the beginning, random methods with guaranteed correctness (i)/(10) percent are used (though practically the probability for correctness is much higher).
	www.math.jussieu.fr /~jmichel/htm/CHAP021.htm (4684 words)

	Christopher Stark, Abstract (Site not responding. Last check: 2007-10-16)
		Algebraic geometers often study nonsmooth varieties by resolving their singularities, and some of the main problems in the area have centered on this technique.
		Group actions have their own singular sets, namely the set of points at which the isotropy (stabilizer) subgroup is not minimal.
		For example, the involution of any Euclidean space which maps x to -x has the origin as its only singular point, while the typical linear cyclic action on a complex vector space has a singular set which is a union of eigenspaces.
	www.math.binghamton.edu /dept/topsem/99Abstracts/stark.html (175 words)

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