Sufficient conditions for the T(T0)-solvability of finite groups

Heliel, A. A. and Al-Shomrani, M. M. Al-Mosa (2012) Sufficient conditions for the T(T0)-solvability of finite groups. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 28 (1). pp. 13-20. ISSN 0866-0174

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Abstract

Let G be a finite group. We say that G is a T0-group if its Frattini quotient group G/Φ(G) is a T-group, where by a T-group we mean a group in which every subnormal subgroup is normal. In this paper, we investigate the structure of the group G if G is the product of two solvable T-groups (T0-groups) H and K such that H permutes with every subgroup of K and K permutes with every subgroup of H (that is, H and K are mutually permutable) and that (|G : H|, |G : K|) = 1. Some structure theorems are also discussed.

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