One-prime power hypothesis for conjugacy class sizes

International Journal of Group Theory

Rachel Camina¹  Alan Camina² 

[1] Fitzwilliam College, University of Cambridge;University of East Anglia;

关键词: conjugacy class sizes;    Finite groups;    insoluble groups;    bipartite graph;   

DOI  :  10.22108/ijgt.2017.12043

来源: DOAJ

【 摘 要 】

A finite group $G$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to $S times A$ where $A$ is abelian and $S cong PSL_2(q)$ for $q in {4,8}$. We confirm this conjecture.

【 授权许可】

Unknown