| Title:
|
Pseudoautomorphisms of Bruck loops and their generalizations (English) |
| Author:
|
Greer, Mark |
| Author:
|
Kinyon, Michael |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
383-389 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that in a weak commutative inverse property loop, such as a Bruck loop, if $\alpha$ is a right [left] pseudoautomorphism with companion $c$, then $c$ [$c^2$] must lie in the left nucleus. In particular, for any such loop with trivial left nucleus, every right pseudoautomorphism is an automorphism and if the squaring map is a permutation, then every left pseudoautomorphism is an automorphism as well. We also show that every pseudoautomorphism of a commutative inverse property loop is an automorphism, generalizing a well-known result of Bruck. (English) |
| Keyword:
|
pseudoautomorphism |
| Keyword:
|
Bruck loop |
| Keyword:
|
weak commutative inverse property |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1256.20062 |
| idMR:
|
MR3017837 |
| . |
| Date available:
|
2012-08-31T11:37:44Z |
| Last updated:
|
2014-10-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142931 |
| . |
| 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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