A Strict Inequality for a Minimal Degree of a Direct Product

2007/08/06 by Neil Saunders, Saunders, Neil
Computer Science · Engineering · Mathematics · #20B05 #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.0708.0714

openalex publication_date 2007/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The minimal faithful permutation degree of a finite group G is the least non-negative integer n such that G embeds in the symmetric group Sym(n). Work of Johnson and Wright established conditions for when the minimal degree of a direct product equals the sum of the minimal degrees for two finite groups. Wright asked whether this is true for all finite groups. A counter- example of degree 15 was provided by the referee and was added as an addendum in a paper of Wright. Here we provide a counter-example of degree 12.

Citations

• The Minimal Degree for a Class of Finite Complex Reflection Groups

Related

• Magma Proof of Strict Inequalities for Minimal Degrees of Finite Groups
• Absorption of Direct Factors With Respect to the Minimal Faithful Permutation Degree of a Finite Group
• Minimal Faithful Permutation Degrees for Irreducible Coxeter Groups and Binary Polyhedral Groups
• The minimal degree of permutation representations of finite groups
• The Minimal Degree for a Class of Finite Complex Reflection Groups