2022/11/17 by Mai Hoang Bien, Peter Danchev, Bien, M. H. +5
Materials Science · Mathematics · #15B33 #16K40 #16U60 #20C07 #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Synthesis and properties of polymers
paper · pdf · doi:10.48550/arxiv.2211.09468
openalex publication_date 2022/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a field with at least three elements and G a locally finite group. This paper aims to show that if either F is algebraically closed or the characteristic of F is positive, then an element in the group algebra FG is a product of unipotent elements if, and only if, it? lies in the first derived subgroup of the unit group of FG. In addition, it? is a product of at most three unipotent elements. Moreover, we explore some crucial properties satisfied by certain algebras like the connection between unipotent elements of index 2 and commutators as well as we investigate the unipotent radical of a group algebra by showing that the group algebra of a finite group over an infinite field cannot have a unipotent maximal subgroup. In particular, we apply these results to twisted group algebras.