Finite exceptional p-groups of small order

Author
Lemieux, Stephane
2007
Keywords
faithful representation , finite exceptional groups , minimal degree , p-groups , permutation groups
Abstract (summary)
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.
Publication Information
Lemieux, S. (2007). Finite exceptional p-groups of small order. COMMUNICATIONS IN ALGEBRA, 35(6), 1890–1894. https://doi.org/10.1080/00927870701246924
Article
English