Frontiers of Mathematics in China >
Regular automorphisms of order p2
Received date: 15 Jan 2019
Accepted date: 05 Sep 2019
Published date: 15 Dec 2019
Copyright
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.
Key words： Polycyclic group; regular automorphism; residually finite
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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