On maximal subgroups of finite groups and theta pairs

Ballester‐Bolinches, A.; Yaoqing, Zhao

doi:10.1080/00927879608825807

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Cited by 6 publications

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“…In [8], Yaoqing improved the definition of θ-pair for a maximal subgroup of a finite group G to a maximal θ-pair and normal θ-pair. He proved that for any maximal subgroup M of a finite group G, there exists a normal maximal θ-pair related to M. The investigationon θ-pair are continued by others in [1,[7][8][9]. Most of ths research deals with the structure of finite groups.…”

Section: Introductionmentioning

confidence: 99%

On the degree of theta pairs of finite groups

Erfanian

2007

ijcms

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Let G be a finite group and M a maximal subgroup of G. pair of subgroups (C, D) satisfying conditions (i) and (iii) and a property thatIn this paper, we introduce the degree of θ-pairs, denoted by dθ(G) as the ratio |θ(G)|/m(G), where θ(G) is the union of all θ-pairs of the maximal subgroups of G and m(G) is the total number of distinct maximal subgroups of G. Similarly, we define the degrees of maximal θ-pairs, θ -pairs and maximal θ -pairs of a finite group G and give some evaluations on the above degrees for some simple groups, nilpotent groups and solvable groups. Moreover, we prove that if G is nilpotent then the degree of maximal θ-pairs of G is exactly 1.

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