Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

New paper accepted by Journal of Algebra

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 f(x) be a non-zero polynomial with integer coefficients. An automorphism \varphi of a group G is said to satisfy the elementary abelian identity f(x) if the linear transformation induced by \varphi on every characteristic elementary abelian section of G is annihilated by f(x). We prove that if a finite (soluble) group G admits a fixed-point-free automorphism \varphi satisfying an elementary abelian identity f(x), where f(x) is a primitive polynomial, then the Fitting height of G is bounded in terms of \deg(f(x)). We also prove that if f(x) is any non-zero polynomial and G is a \sigma'-group for a finite set of primes \sigma=\sigma(f(x)) depending only on f(x), then the Fitting height of G is bounded in terms of the number irr(f(x)) of different irreducible factors in the decomposition of f(x). These bounds for the Fitting height are stronger than the well-known bounds in terms of the composition length \alpha (|\varphi|) of \langle\varphi\rangle when \deg f(x) or irr(f(x)) is small in comparison with \alpha (|\varphi|).

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This entry was posted on July 7, 2022 by in New publications, research.

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