| Title:
|
Automorphic loops and metabelian groups (English) |
| Author:
|
Greer, Mark |
| Author:
|
Raney, Lee |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
523-534 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a uniquely 2-divisible group $G$, we study a commutative loop $(G,\circ)$ which arises as a result of a construction in ``Engelsche elemente noetherscher gruppen'' (1957) by R. Baer. We investigate some general properties and applications of ``$\circ$'' and determine a necessary and sufficient condition on $G$ in order for $(G, \circ)$ to be Moufang. In ``A class of loops categorically isomorphic to Bruck loops of odd order'' (2014) by M. Greer, it is conjectured that $G$ is metabelian if and only if $(G, \circ)$ is an automorphic loop. We answer a portion of this conjecture in the affirmative: in particular, we show that if $G$ is a split metabelian group of odd order, then $(G, \circ)$ is automorphic. (English) |
| Keyword:
|
metabelian groups |
| Keyword:
|
automorphic loops |
| Keyword:
|
Bruck loops |
| Keyword:
|
Moufang loops |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 07332726 |
| idMR:
|
MR4230957 |
| DOI:
|
10.14712/1213-7243.2020.043 |
| . |
| Date available:
|
2021-02-25T12:43:17Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148662 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
