Tom\'a\v s Kepka, Petr N\v emec
Connected transversals --- the Zassenhaus case

Comment.Math.Univ.Carolinae 41,2 (2000) 299-300.

Abstract:In this short note, it is shown that if $A,B$ are $H$-connected transversals for a finite subgroup $H$ of an infinite group $G$ such that the index of $H$ in $G$ is at least 3 and $H\cap H^u\cap H^v=1$ whenever $u,v\in G\setminus H$ and $uv^{-1}\in G\setminus H$ then $A=B$ is a normal abelian subgroup of $G$.

Keywords: group, subgroup, connected transversals, core
AMS Subject Classification: 20F12, 20D60