A generalization of Neumann's Question

2017/12/30 by A. Ahmadkhah, Ahmadkhah, A., Soran Marzang +3
Computer Science · Engineering · Mathematics · #16U80 #20D10 #20G15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1801.00113

openalex publication_date 2017/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group, m≥2 and n≥1. We say that G is an T(m,n)-group if for every m subsets X₁, X₂, …, X_m of G of cardinality n, there exists i≠ j and x_i ∈ X_i, x_j ∈ X_j such that x_ix_j=x_jx_i. In this paper, we give some examples of finite and infinite non-abelian T(m,n)-groups and we discuss finiteness and commutativity of such groups. We also show solvability length of a solvable T(m,n)-group is bounded in terms of m and n.

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