منابع مشابه
Supersoluble Groups
We shall term a group G supersoluble if every homomorphic image H9*l of G contains a cyclic normal subgroup different from 1. Supersoluble groups with maximum condition, in particular finite supersoluble groups, have been investigated by various authors: Hirsch, Ore, Zappa and more recently Huppert and Wielandt. In the present note we want to establish the close connection between supersoluble ...
متن کاملSome numerical results on two classes of finite groups
In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...
متن کاملA Class of Generalized Supersoluble Groups
This paper is devoted to the study of groups G in the universe cL̄ of all radical locally finite groups with min-p for all primes p such that every δ-chief factor of G is either a cyclic group of prime order or a quasicyclic group. We show that within the universe cL̄ this class of groups behaves very much as the class of finite supersoluble groups.
متن کاملsome numerical results on two classes of finite groups
in this paper, we consider the finitely presented groups $g_{m}$ and $k(s,l)$ as follows;$$g_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$k(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...
متن کاملLanguages Recognized by Finite Supersoluble Groups
In this paper, we give two descriptions of the languages recognized by finite supersoluble groups. We first show that such a language belongs to the Boolean algebra generated by the modular products of elementary commutative languages. An elementary commutative language is defined by a condition specifying the number of occurrences of each letter in its words, modulo some fixed integer. Our sec...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.07.035