Finite exceptional p-groups of small order
faithful representation, finite exceptional groups, minimal degree, p-groups, permutation groups
A finite group is said to be exceptional if its minimal degree of a faithful permutation representation is strictly less than that of one of its factor groups, called a distinguished quotient. It was previously unknown if exceptional p-groups of order less than p 6 existed for p an odd prime. The author proved in his M.Sc thesis that there are none of order ≤p 4 and gave restrictions on the possible existence of distinguished quotients of exceptional groups of order p 5. In this article, an exceptional p-group of order p 5 is exhibited for p any odd prime.
Lemieux, S. (2007). Finite exceptional p-groups of small order. COMMUNICATIONS IN ALGEBRA, 35(6), 1890–1894. https://doi.org/10.1080/00927870701246924
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