Bulletin of the Australian Mathematical Society

Table of Contents - February 2009 - Volume 79, Issue 01  

Research Article

STRICT INEQUALITIES FOR MINIMAL DEGREES OF DIRECT PRODUCTS

NEIL SAUNDERSa1

a1 School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia (email: neils@maths.usyd.edu.au)

Abstract

The minimal faithful permutation degree μ(G) 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 in the 1970s established conditions for when μ(H×K)=μ(H)+μ(K), for finite groups H and K. 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 Wright’s paper. Here we provide two counter-examples; one of degree 12 and the other of degree 10.

(Received March 17 2008)

2000 Mathematics subject classification

  • primary 20B35; secondary 51F15

Keywords and phrases

  • faithful permutation representations;
  • complex reflection groups;
  • monomial reflection groups