| Title:
|
Connected transversals -- the Zassenhaus case (English) |
| Author:
|
Kepka, Tomáš |
| Author:
|
Němec, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
299-300 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $G$. (English) |
| Keyword:
|
group |
| Keyword:
|
subgroup |
| Keyword:
|
connected transversals |
| Keyword:
|
core |
| MSC:
|
20D60 |
| MSC:
|
20E07 |
| MSC:
|
20F12 |
| MSC:
|
20F99 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1038.20022 |
| idMR:
|
MR1780873 |
| . |
| Date available:
|
2009-01-08T19:01:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119165 |
| . |
| Reference:
|
[1] Drápal A.: Multiplication groups of free loops I.Czech. Math. J. 46 (121) (1996), 121-131. MR 1371694 |
| Reference:
|
[2] Drápal A.: Multiplication groups of free loops II.Czech. Math. J. 46 (121) (1996), 201-220. MR 1388610 |
| Reference:
|
[3] Drápal A.: Multiplication groups of finite loops that fix at most two points.submitted. |
| . |
