Finite groups admitting a coprime automorphism satisfying an additional polynomial identity
Wolfgang Alexander Moens

TL;DR
This paper extends classical results on finite groups with coprime automorphisms by establishing bounds on the soluble radical's Fitting height and index when automorphisms satisfy polynomial identities, with explicit bounds especially for small degrees.
Contribution
It generalizes known bounds for automorphisms of coprime order to cases where automorphisms satisfy polynomial identities, providing explicit bounds based on polynomial degree.
Findings
Bound on Fitting height of the soluble radical
Bound on the index of the soluble radical
Explicit bounds for small polynomial degrees
Abstract
It is known that a finite group with an automorphism of coprime order has a soluble radical of -bounded Fitting height and index. We extend this classic result as follows. Let be a primitive polynomial and let be a finite group with an automorphism of coprime order satisfying , for all . Then the soluble radical of has -boundex Fitting height and index. The bounds are made explicit and are particularly good for small values of the degree .
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Taxonomy
TopicsFinite Group Theory Research
