Year: 2026
Type: preprint
Abstract: Let H be a linear group. We show that if there is an invertible matrix x such that all the elements of xH share the same characteristic polynomial then H is virtually solvable. There are plenty of applications that will be presented in future paper. Here, we discuss some applications to the generalized Weigold conjecture and present an alternative straightforward proof of the Formanek--Procesi nonlinearity theorem for Aut(F_n), n>2, over every field. When n>4 our non-linearity proof gives a stronger result than the original Formanek--Procesi theorem.
Source: arXiv (Cornell University)
Authors: Avni, Nir, Gelander, Tsachik
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214218853