Finite groups with seminormal or abnormal Sylow subgroups

Document Type: Research Paper

Authors

1 Francisk Skorina Gomel State University, Department of Mathematics, Sovetskaya str., 104, Gomel, 246019, Republic of Belarus

2 Physic and Mathematic Department, Brest State A.S. Pushkin University, Brest, Belarus

Abstract

‎Let $G$ be a finite group in which every Sylow subgroup‎ ‎is seminormal or abnormal‎. ‎We prove that $G$ has a Sylow tower‎. ‎We establish that if a group has a maximal subgroup ‎‎‎‎with Sylow subgroups under the same conditions‎, ‎then this group is soluble‎.

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