Trifactorisable groups

Author:

Pennington Elizabeth

Abstract

The group G is called trifactorisable if G has three subgroups, A, B, and C such that G = AB = BC = CA. Obviously the structure of the group G will be restricted by the structure of these subgroups. In this paper it will be shown that a finite group G is π-separable if and only if it satisfies Dπ and has a trifactorisation with two factors π closed and the third, C say, π-separable. In this case we show that the π- and π-lengths of G can be at most one more than those of C, and so it is this factor which “controls” the structure of G. Similar results are proved for π-solubility and solubility.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Factorizations of Finite Groups and Related Topics;Algebra Colloquium;2020-02-25

2. Arithmetic Graphs and Classes of Finite Groups;Siberian Mathematical Journal;2019-01

3. FINITE TRIFACTORISED GROUPS AND -DECOMPOSABILITY;Bulletin of the Australian Mathematical Society;2018-01-31

4. On permuteral subgroups in finite groups;Siberian Mathematical Journal;2014-03

5. On Products of Nonnormal Subgroups of Finite Soluble Groups;Acta Applicandae Mathematicae;2005-01

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