Year: 2026
Type: preprint
Abstract: Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$, where $p$ is an odd prime. Let $*$ be the classical involution of $FG$ and let $FG^-$ be the Lie subalgebra of the skew symmetric elements with respect to $*$. In this paper, we prove that the Lie nilpotency index of $FG$ is determined by its Lie subalgebra $FG^-$, in the case when $G$ is a $p$-group with a commutator subgroup of order $p$. The structure of the terms of the lower Lie central series of $FG^-$ has also been described.
Source: arXiv (Cornell University)
Author: Balogh, Zsolt Adam
Institution: United Arab Emirates University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: United Arab Emirates University
Award: G6018698427
OpenAlex ID: W7204867919