Geodesic
Connected transversals -- the Zassenhaus case
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 299-300.

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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 $G$.
Classification : 20D60, 20E07, 20F12, 20F99, 20N05
Keywords: group; subgroup; connected transversals; core 
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     title = {Connected transversals -- the {Zassenhaus} case},
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Kepka, Tomáš; Němec, Petr. Connected transversals -- the Zassenhaus case. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 299-300. http://geodesic.mathdoc.fr/item/CMUC_2000__41_2_a8/