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Topic: Permutation group

	groups
		Examples of Finite Groups: A = {1, -1, i, -i} where * is multiplication, B = {0, 1, 2, 3) where * is addition modulo 4.
		A subgroup is a group entirely inside another: {1, -1} is a subgroup of A, {0, 2) is is a subgroup of B.
		The makers of GAP have written an analysis of Rubik's Cube from a Group Theory perspective.
	www.mathpuzzle.com /groups.html (581 words)

	No Title
		Doubly transitive permutation groups in which the one-point stabilizer is triply transitive on a set of blocks, J.
		Primitive permutation groups with a common suborbit, and edge-transitive graphs, (with M.W. Liebeck and J. Saxl), Proc.
		Permutation groups and normal subgroups, Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002.
	www.maths.uwa.edu.au /~praeger/CV/cherylpubs (5292 words)

	Group Theory & Rubik's Cube
		Group theory is the study of the algebra of transformations and symmetry.
		Given an element x of a group G, the orbit of x is the set of all elements of G which are generated by x, i.e.
		A representation of a group G is a set of matrices M which are homomorphic to the group.
	akbar.marlboro.edu /~mahoney/courses/Spr00/rubik.html (3602 words)

	Abstracts of papers by Peter J. Cameron
		We introduce the concept of orbit-homogeneity of permutation groups: a group G is orbit t-homogeneous if two sets of cardinality t lie in the same orbit of G whenever their intersections with each G-orbit have the same cardinality.
		Every permutation group which is not 2-transitive acts on a nontrivial coherent configuration, but the question of which permutation groups G act on nontrivial association schemes (symmetric coherent configurations) is considerably more subtle.
		After a brief discussion of the semilattice of subpermutations (partial permutations), I conclude with a concept to replace that of "random permutation" in the infinite case: for countable sets, there is a unique such object (this is the analogue of the Erdös-Rényi theorem on the countable random graph).
	www.maths.qmul.ac.uk /~pjc/abstracts.html (8221 words)

	Micro biography of (Site not responding. Last check: 2007-11-06)
		On the group of a graph with respect to a subgraph.
		(E.M. Palmer) On the automorphism group of a composite graph.
		The collaboration graph of mathematicians and a conjecture of Erdos.
	www.cs.nmsu.edu /~fnh/publ.html (3284 words)

	Works Citing the On-Line Encyclopedia of Integer Sequences
		Bauer, Triangular monoids and an analog to the derived sequence of a solvable group.
		Gilbey,Permutation Group Algebras and Parking Functions, PHD thesis, 2002.
		Myers, Counting permutations by their rigid patterns, J. Combin.
	www.research.att.com /~njas/sequences/cite.html (8806 words)

	References for Methods of Computational Group Theory
		David Johnson's book [Jo97] is a very readable introduction to the general subject of fp groups touching computational aspects.
		The authoritative text on the subject of computing methods for fp groups is the book [Si94] by Charles C. Sims.
		We refrain from listing any of the several hundred papers having contributed to the development of algorithms in computational group theory.
	www.gap-system.org /Doc/references.html (535 words)

	Bicube / Bandaged Rubik's Cube (Site not responding. Last check: 2007-11-06)
		It is a little like the Square One puzzle, in that the possible positions do not mathematically form a group.
		Nearly all other moving piece puzzles do form groups because they are in effect (isomorphic to subgroups of) permutation groups, usually generated by the simplest possible moves.
		Any sequence of moves that permutes the pieces, bringing them back to the same configuration must have an even number of quarter face turns to bring the free corner back to its original position, and therefore must be an even permutation on the seven glued corner pieces.
	www.geocities.com /jaapsch/puzzles/bandage.htm (1965 words)

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