Powers in finite unitary groups

2023/04/26 by Saikat Panja, Anupam Singh, Panja, Saikat +1 · 2 citations
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2304.13735

Abstract

Let U(n,\mathbbF_q²) denote the subgroup of unitary matrices of the general linear group GL(n,\mathbbF_q²) which fixes a Hermitian form and M≥ 2 an integer. This is a companion paper to the previous works where the elements of the groups GL(n,\mathbbF_q), Sp(2n,\mathbbF_q), O^±(2n,\mathbbF_q) and O(2n+1,\mathbbF_q) which has an M-th root in the concerned group, have been described. Here we will describe the M-th powers in unitary groups for the regular semisimple, semisimple and cyclic elements. Our methods are parallel to those of the Memoir ``A generating function approach to the enumeration of matrices in classical groups over finite fields" by Fulman, Neumann and Praeger.

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• Dynamics of Word Maps on Groups and Polynomial Maps on Algebras
• Power maps on General Linear groups over finite principal ideal local rings of length two

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