Regular automorphisms of order p2

doi:10.1007/s11464-019-0790-8

Front. Math. China

2019, Vol. 14

Issue (6) : 1367-1373 https://doi.org/10.1007/s11464-019-0790-8

RESEARCH ARTICLE

Regular automorphisms of order p²

Tao XU¹, Heguo LIU²(

)

¹. Department of Science, Hebei University of Engineering, Handan 056038, China
². Department of Mathematics, Hubei University, Wuhan 430062, China

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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 g^ϕ= [g,α] is surjective, then G is soluble. If G is polycyclic, then C_G(α^p) and G/[G,α^p] are both nilpotent-by-finite.

Keywords Polycyclic group regular automorphism residually finite

Corresponding Author(s): Heguo LIU

Issue Date: 07 January 2020

Cite this article:

Tao XU,Heguo LIU. Regular automorphisms of order p²[J]. Front. Math. China, 2019, 14(6): 1367-1373.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0790-8
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I6/1367

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