A Strict Inequality for a Minimal Degree of a Direct Product

Details A Strict Inequality for a Minimal Degree of a Direct Product A Strict Inequality for a Minimal Degree of a Direct Product

2007-08-06

arxiv.org/abs/0708.0714v2

Mathematics

Group Theory

8 pages

Scientific paper

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.

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