Connected transversals -- the Zassenhaus case

Kepka, Tomáš, and Němec, Petr. "Connected transversals -- the Zassenhaus case." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 299-300. <http://eudml.org/doc/248598>.

@article{Kepka2000,
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 $G$.},
author = {Kepka, Tomáš, Němec, Petr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {group; subgroup; connected transversals; core; connected transversals; normal abelian subgroups},
language = {eng},
number = {2},
pages = {299-300},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Connected transversals -- the Zassenhaus case},
url = {http://eudml.org/doc/248598},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Kepka, Tomáš
AU - Němec, Petr
TI - Connected transversals -- the Zassenhaus case
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 299
EP - 300
AB - 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 $G$.
LA - eng
KW - group; subgroup; connected transversals; core; connected transversals; normal abelian subgroups
UR - http://eudml.org/doc/248598
ER -