Abstract
A group is called a T-group if all its subnormal subgroups are normal. Finite T-groups have been widely studied since the seminal paper of Gaschütz (J. Reine Angew. Math. 198 (1957), 87–92), in which he described the structure of finite solvable T-groups. We call a finite group G an NNM-group if each non-normal subgroup of G is contained in a non-normal maximal subgroup of G. Let G be a finite group. Using the concept of NNM-groups, we give a necessary and sufficient condition for G to be a solvable T-group (Theorem 1), and sufficient conditions for G to be supersolvable (Theorems 5, 7 and Corollary 6).
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Kaplan, G. On T-groups, supersolvable groups, and maximal subgroups. Arch. Math. 96, 19–25 (2011). https://doi.org/10.1007/s00013-010-0207-0
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DOI: https://doi.org/10.1007/s00013-010-0207-0