Powers in finite unitary groups

Abstract

Let U(n, Fq2 ) denote the subgroup of unitary matrices of the general linear group GL(n, Fq2 ) which fix a Hermitian form and let M >= 2 be an integer. In earlier work, elements of the groups GL(n, Fq), Sp(2n, Fq), O +/-(2n, Fq) and O (2n + 1, Fq) with an M-th root have been described. Here we will describe the M-th powers in unitary groups for the regular semisimple, semisimple and cyclic elements, under the assumption that M and q are coprime. We will further describe the generating functions in the corresponding cases. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.