Groups with relatively small normalizers of primary subgroups

V. A. Antonov

National Research South Ural State University, Chelyabinsk, Russia

Abstract: The structure of finite groups $G$ is studied in which for every primary subgroup $A$, almost all of its automorphisms induced by elements of $G$ are inner. Namely, for any such subgroup, the index $|N(A):A\cdot C(A)|$ divides some prime number. These groups are called $NSP$-groups.

Keywords: finite group, inner automorphism, $NSP$-group.

UDC: 512.54

Received: 04.05.2010

 English version: Algebra and Logic, 2012, 51:5, 375–383

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