| Title:
|
Moufang semidirect products of loops with groups and inverse property extensions (English) |
| Author:
|
Greer, Mark |
| Author:
|
Raney, Lee |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
411-420 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S. Gagola III, Cyclic extensions of Moufang loops induced by semiautomorphisms, J. Algebra Appl. 13 (2014), no. 4, 1350128], but from an external point of view. (English) |
| Keyword:
|
extensions |
| Keyword:
|
semidirect products |
| Keyword:
|
Moufang loops |
| Keyword:
|
inverse property loops |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06391551 |
| idMR:
|
MR3225618 |
| . |
| Date available:
|
2015-01-19T10:56:08Z |
| Last updated:
|
2016-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143816 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Chein O.: Moufang loops of small order. I.Trans. Amer. Math. Soc. 188 (1974), 31–51. Zbl 0286.20088, MR 0330336, 10.1090/S0002-9947-1974-0330336-3 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Gagola S. III: Cyclic extensions of Moufang loops induced by semiautomorphisms.J. Algebra Appl. 13 (2014), no. 4, 1350128. MR 3153863, 10.1142/S0219498813501284 |
| 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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| . |
