Minimal Faithful Quasi-Permutation Representation Degree of p-Groups with Cyclic Center

2023/02/13 by Sunil Kumar Prajapati, Prajapati, Sunil Kumar, Ayush Udeep +1
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2302.06257

Abstract

For a finite group G, we denote by μ(G), and c(G), the minimal degree of faithful permutation representation of G, and the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C, respectively. In this article, we study μ(G), and c(G) for various classes of finite non-abelian p-groups with cyclic center. We prove a result for normally monomial p-groups with cyclic center which generalizes a result of Behravesh for finite p-groups of nilpotency class 2 with cyclic center [5, Theorem 4.12]. We also compute minimal degrees for some classes of metabelian p-groups.

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