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FINITE GROUPS WITH A CYCLIC NORM QUOTIENT

  • Wang, Junxin
  • Received : 2015.02.22
  • Published : 2016.03.31

Abstract

The norm N(G) of a group G is the intersection of the normalizers of all the subgroups of G. In this paper, the structure of finite groups with a cyclic norm quotient is determined. As an application of the result, an interesting characteristic of cyclic groups is given, which asserts that a finite group G is cyclic if and only if Aut(G)/P(G) is cyclic, where P(G) is the power automorphism group of G.

Keywords

norm;cyclic group;power automorphism

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Acknowledgement

Supported by : National Natural Science Foundation of China