%A XU Tao
%T A note on polynomial automorphisms
%0 Journal Article
%D 2020
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2020.005
%P 52-54
%V 55
%N 10
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3347.shtml}
%8 2020-10-20
%X A polynomial automorphism of a group *G* is an automorphism of the formx|→(v^{-1}_{1}x^{ε1}v_{1})(v^{-1}_{2}x^{ε2}v_{2})…(v^{-1}_{m}x^{εm}v_{m}),where *ε*_{i}=±1 and *v*_{}1*,v*_{}2*,…,v*_{m} 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≤2*d*).