| Title:
|
On the solvability of commutative loops and their multiplication groups (English) |
| Author:
|
Myllylä, Kari |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
209-213 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the situation when the inner mapping group of a commutative loop is of order $2p$, where $p=4t+3$ is a prime number, and we show that then the loop is solvable. (English) |
| Keyword:
|
solvability |
| Keyword:
|
loop |
| Keyword:
|
group |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 0983.20011 |
| idMR:
|
MR1732641 |
| . |
| Date available:
|
2009-01-08T18:51:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119076 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Herstein I.N.: A remark on finite groups.Proc. Amer. Math. Soc. 9 (1958), 255-257. Zbl 0089.01601, MR 0093542 |
| Reference:
|
[4] Neumann P.M., Stoy G., Thompson E.: Groups and Ggeometry.Oxford University Press, 1994. MR 1283590 |
| Reference:
|
[5] Niemenmaa M.: Transversals, commutators and solvability in finite groups.Bollettino U.M.I. (7) 9-A (1995), 203-208. Zbl 0837.20026, MR 1324621 |
| Reference:
|
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| Reference:
|
[7] Niemenmaa M.: On connected transversals to subgroups whose order is a product of two primes.European J. Comb. 18 (1997), 915-919. Zbl 0889.20044, MR 1485376 |
| Reference:
|
[8] Niemenmaa M., Kepka T.: On multiplication groups of loops.J. Algebra 135 (1990), 112-122. Zbl 0706.20046, MR 1076080 |
| Reference:
|
[9] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups.Bull. Australian Math. Soc. 49 (1994), 121-128. Zbl 0799.20020, MR 1262682 |
| Reference:
|
[10] Niemenmaa M., Vesanen A.: On subgroups, transversals and commutators.in Proceeding of the Groups Galway/St. Andrews 1993, London Math. Soc. Lecture Notes Series 212 (1995), pp.476-481. Zbl 0862.20023, MR 1337289 |
| Reference:
|
[11] Vesanen A.: Solvable groups and loops.J. Algebra 180 (1996), 862-876. Zbl 0853.20050, MR 1379214 |
| . |
