### 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.

Original language | English |
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Pages (from-to) | 23-30 |

Number of pages | 8 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 79 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2009 |

### Keywords

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

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## Cite this

Saunders, N. J. (2009). Strict inequalities for minimal degrees of direct products.

*Bulletin of the Australian Mathematical Society*,*79*(1), 23-30. https://doi.org/10.1017/S0004972708000956