GROUPS AND LIE-ALGEBRAS WITH ALMOST REGULAR AUTOMORPHISMS

[摘要] It is proved that if a locally nilpotent group G admits an almost regular automorphism of prime order p then G contains a nilpotent subgroup G1 such that \G:G1\ less-than-or-equal-to (p, m) and the class of nilpotency of G1 less-than-or-equal-to g(p), where f is a function on p and the number of fixed elements m and g depends on p only. An analog is proved for Lie rings (not necessarily locally nilpotent). These give an affirmative answer to the questions raised by Khukhro. (C) 1994 Academic Press, Inc.

[发布日期] 1994-03-15