New paper by Evgeny Khukhro (Univ. of Lincoln) and Wolfgang Moens† (University of Vienna) “Fitting height of finite groups admitting a fixed-point-free automorphism satisfying an additional polynomial identity” has been accepted for publication in Journal of Algebra.
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†The second author died in May 2022.
Abstract: Let be a non-zero polynomial with integer coefficients. An automorphism
of a group
is said to satisfy the elementary abelian identity
if the linear transformation induced by
on every characteristic elementary abelian section of
is annihilated by
. We prove that if a finite (soluble) group
admits a fixed-point-free automorphism
satisfying an elementary abelian identity
, where
is a primitive polynomial, then the Fitting height of
is bounded in terms of
. We also prove that if
is any non-zero polynomial and
is a
-group for a finite set of primes
depending only on
, then the Fitting height of
is bounded in terms of the number irr
of different irreducible factors in the decomposition of
. These bounds for the Fitting height are stronger than the well-known bounds in terms of the composition length
of
when
or irr
is small in comparison with
.