2015•Journal of Algebra and Its ApplicationsRequires access

Finite groups with each non-normal subgroup having maximal normal cores

Heng Lv, Zhibo Shao, Wei Zhou

Abstract

In this paper, we study a finite group [Formula: see text] such that [Formula: see text] is a prime for each non-normal subgroup [Formula: see text] of [Formula: see text]. We prove that such a group must contain a big abelian subgroup. More specifically, if such a group [Formula: see text] is not supersoluble, then there is an abelian subgroup [Formula: see text] such that [Formula: see text], and if [Formula: see text] is supersoluble, then there is an abelian subgroup [Formula: see text] such that [Formula: see text] or [Formula: see text], where [Formula: see text] and [Formula: see text] are primes.

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Key concepts: Mathematics, Characteristic subgroup, Normal subgroup, Combinatorics, Abelian group, Torsion subgroup, Prime (order theory), Group (periodic table)