| Title:
|
A class of commutative loops with metacyclic inner mapping groups (English) |
| Author:
|
Drápal, Aleš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
357-382 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate loops defined upon the product $\Bbb Z_m\times \Bbb Z_k$ by the formula $(a,i)(b,j) = ((a+b)/(1+tf^i(0)f^j(0)), i + j)$, where $f(x) = (sx + 1)/(tx+1)$, for appropriate parameters $s,t \in \Bbb Z_m^*$. Each such loop is coupled to a 2-cocycle (in the group-theoretical sense) and this connection makes it possible to prove that the loop possesses a metacyclic inner mapping group. If $s=1$, then the loop is an A-loop. Questions of isotopism and isomorphism are considered in detail. (English) |
| Keyword:
|
A-loop |
| Keyword:
|
nucleus |
| Keyword:
|
inner mapping group |
| Keyword:
|
cocycle |
| Keyword:
|
linear fractional |
| MSC:
|
08A05 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1192.20053 |
| idMR:
|
MR2490433 |
| . |
| Date available:
|
2009-05-05T17:11:49Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119729 |
| . |
| 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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| . |
