School of Mathematics & Physics, University of Lincoln
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.
†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 .