| Title:
|
On dicyclic groups as inner mapping groups of finite loops (English) |
| Author:
|
Leppälä, Emma |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
549-553 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group with a dicyclic subgroup $H$. We show that if there exist $H$-connected transversals in $G$, then $G$ is a solvable group. We apply this result to loop theory and show that if the inner mapping group $I(Q)$ of a finite loop $Q$ is dicyclic, then $Q$ is a solvable loop. We also discuss a more general solvability criterion in the case where $I(Q)$ is a certain type of a direct product. (English) |
| Keyword:
|
solvable loop |
| Keyword:
|
inner mapping group |
| Keyword:
|
dicyclic group |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06674896 |
| idMR:
|
MR3583306 |
| DOI:
|
10.14712/1213-7243.2015.180 |
| . |
| Date available:
|
2017-01-09T22:19:45Z |
| Last updated:
|
2019-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145948 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| . |
