# Connected transversals -- the Zassenhaus case

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 2, page 299-300
- ISSN: 0010-2628

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topKepka, 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 -

## References

top- Drápal A., Multiplication groups of free loops I, Czech. Math. J. 46 (121) (1996), 121-131. (1996) MR1371694
- Drápal A., Multiplication groups of free loops II, Czech. Math. J. 46 (121) (1996), 201-220. (1996) MR1388610
- Drápal A., Multiplication groups of finite loops that fix at most two points, submitted.

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