منابع مشابه
Enumeration of Double Cosets
Let H and K be subgroups of a group G. The double cosets of H and K in G are the sets HgK, g E G. In this paper we describe a procedure, P, for determining the cardinality of the set H\G/K of double cosets of H and K in G given a finite presentation for G and finite sets of generators for H and K. It is well known that the problem of determining whether or not a group G defined by a finite pres...
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If a soluble group G contains two finitely generated abelian subgroups A, B such that the number of double cosets AgB is finite, then G is shown to be virtually polycyclic.
متن کاملThe Double Cosets of a Finite Group
1. Introduction. It is the purpose of this paper to study some of the properties of the double cosets of a finite group and to prove two main theorems which generalize the results of two previous papers by the author, 2 giving some relations between the double cosets and the irreducible components of the permutation group generated by a given subgroup. We let H be an arbitrary but fixed subgrou...
متن کاملConstructive graph labeling using double cosets
Two efficient computer implemented algorithms are presented -=. :'or explicitly constructing all distinct labelings of a graph G :;ith a set of (not necessarily distinct) labels L , given the _;ymmetry group B of G . Two recursive reductions of the problem ,?_rld a precomputation involving certain orbits of stabilizer subgroups q--e the LAtechniques used by the algorithm. Moreover, for each la3...
متن کاملParabolic Double Cosets in Coxeter Groups
Parabolic subgroups WI of Coxeter systems (W,S), as well as their ordinary and double quotients W/WI and WI\W/WJ , appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of regular polytopes. The set of ordinary cosets wWI , for I ⊆ S, forms the Coxeter complex of W , and is well-studied. In this article...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1982
ISSN: 0022-4049
DOI: 10.1016/0022-4049(82)90023-8