Finite number of double cosets in a free product with amalgamation
نویسندگان
چکیده
منابع مشابه
The 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...
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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 کاملEnumeration 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...
متن کاملOn pm$^+$ and finite character bi-amalgamation
Let $f:Arightarrow B$ and $g:A rightarrow C$ be two ring homomorphisms and let $J$ and $J^{'}$ be two ideals of $B$ and $C$, respectively, such that $f^{-1}(J)=g^{-1}(J^{'})$. The bi-amalgamation of $A$ with $(B,C)$ along $(J,J^{'})$ with respect of $(f,g)$ is the subring of $Btimes C$ given by $Abowtie^{f,g}(J,J^{'})={(f(a)+j,g(a)+j^{'})/ a in A, (j,j^{'}) in Jtimes J^{'}}.$ In ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0529204-3