JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (10): 52-54.doi: 10.6040/j.issn.1671-9352.0.2020.005

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A note on polynomial automorphisms

XU Tao   

  1. Department of Science, Hebei University of Engineering, Handan 056038, Hebei, China
  • Online:2020-10-20 Published:2020-10-07

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Abstract: A polynomial automorphism of a group G is an automorphism of the formx|→(v-11xε1v1)(v-12xε2v2)…(v-1mxεmvm),where εi=±1 and v1,v2,…,vm are fixed elements in G. In this paper we prove that if G is a(nilpotent of class c)-by-(soluble of derived length d)group, then the group generated by the polynomial automorphism of G is(nilpotent of class≤c-1)-by-(soluble of derived length≤2d).

Key words: polynomial automorphism, nilpotnet group, nilpotent-by-Abelian group, nilpotent-by-metabelian group

CLC Number: 

  • O152
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