RESEARCH ARTICLE

Regular automorphisms of order p2

  • Tao XU 1 ,
  • Heguo LIU , 2
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  • 1. Department of Science, Hebei University of Engineering, Handan 056038, China
  • 2. Department of Mathematics, Hubei University, Wuhan 430062, China

Received date: 15 Jan 2019

Accepted date: 05 Sep 2019

Published date: 15 Dec 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

Let G be a group, and let α be a regular automorphism of order p2 of G, where p is a prime. If G is polycyclic-by-finite and the map ϕ : G G defined by gϕ= [g,α] is surjective, then G is soluble. If G is polycyclic, then CG(αp) and G/[G,αp] are both nilpotent-by-finite.

Cite this article

Tao XU , Heguo LIU . Regular automorphisms of order p2[J]. Frontiers of Mathematics in China, 2019 , 14(6) : 1367 -1373 . DOI: 10.1007/s11464-019-0790-8

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