Finite groups with subnormal non-cyclic subgroups

Abstract

In this paper we consider finite groups G such that every non-cyclic maximal subgroup in its Sylow subgroups is subnormal in G. In particular, we prove that such solvable groups have an ordered Sylow tower.

On p-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups

“…Let M(G) be the set of all maximal subgroups of Sylow subgroups of a group G. One of the first results related to the study of the structure of a group with given restrictions on M(G) belongs to Srinivasan, see [3]. In particular, in [3] it is proved that a group G is supersolvable, if every subgroup of M(G) is normal in G. Subsequently, groups with restrictions on subgroups of M(G) have been studied in the works of many authors, see the literature in [4].…”