Paper Information

Journal:   JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY)   WINTER 2010 , Volume - , Number 74/2 (MATHEMATICS ISSUE); Page(s) 19 To 25.
 
Paper: 

X-DECOMPOSABLE FINITE GROUPS

 
Author(s):  YAVARI M.*, ASHRAFI A.R.
 
* MATHEMATICS DEPARTMENT, KASHAN BRANCH, ISLAMIC AZAD UNIVERSITY, KASHAN, IRAN
 
Abstract: 
Introduction: Let G be a finite group and A be a normal subgroup of G. We denote by nee(A) the number of G-conjugacy classes of A and A is called n-decomposable, if ncc (A) = n. Set Ncc(G) = {ncc(A) | A D G}. Let X be a nonempty subset of positive integers. A group G is called X-decomposable, if Nee(G) =X.
Aim: The aim of this paper is finding all subsets X of positive integers such that there is a X-decomposable finite group.
Materials and Methods: In this paper, by using a method of Shahryari and Shahabi given in [10], we first obtain the center of the groups under consideration and then by applying some results of Karpilovsky, the characterization of the groups is obtained.
Results: We first characterize the solvable n-decomposable finite groups and then by using some results of Breuer in the classification of finite simple groups, the characterization of n-decomposable finite groups, 1
£n£8, are given.
Conclusion: Using the methods presented here and some complicated calculations, it is possible to solve the problem for n
£12.
 
Keyword(s): N-DECOMPOSABLE SUBGROUP, CONJUGACY CLASS, X-DECOMPOSABLE GROUP
 
References: 
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