Strict inequalities for minimal degrees of direct products

Neil J Saunders

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)23-30
Number of pages8
JournalBulletin of the Australian Mathematical Society
Issue number1
Publication statusPublished - Feb 2009


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


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