| Title:
|
On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops (English) |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
189-193 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group. (English) |
| Keyword:
|
loop |
| Keyword:
|
dihedral group |
| Keyword:
|
inner mapping group |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06940862 |
| idMR:
|
MR3815684 |
| DOI:
|
10.14712/1213-7243.2015.234 |
| . |
| Date available:
|
2018-06-28T08:41:43Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147251 |
| . |
| Reference:
|
[1] Bruck R. H.: Contributions to the theory of loops.Trans. Amer. Math. Soc. 60 (1946), 245–354. Zbl 0061.02201, MR 0017288, 10.1090/S0002-9947-1946-0017288-3 |
| Reference:
|
[2] Drápal A.: A class of commutative loops with metacyclic inner mapping groups.Comment. Math. Univ. Carolin. 49 (2008), no. 3, 357–382. MR 2490433 |
| Reference:
|
[3] Niemenmaa M.: Finite loops with nilpotent inner mapping groups are centrally nilpotent.Bull. Aust. Math. Soc. 79 (2009), no. 1, 109–114. Zbl 1167.20039, MR 2486887, 10.1017/S0004972708001093 |
| Reference:
|
[4] Niemenmaa M.: On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^4$.Comment. Math. Univ. Carolin. 51 (2010), no. 4, 559–563. MR 2858260 |
| Reference:
|
[5] Niemenmaa M., Kepka T.: On multiplication groups of loops.J. Algebra 135 (1990), no. 1, 112–122. Zbl 0706.20046, MR 1076080, 10.1016/0021-8693(90)90152-E |
| Reference:
|
[6] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups.Bull. Austral. Math. Soc. 49 (1994), no. 1, 121–128. Zbl 0799.20020, MR 1262682, 10.1017/S0004972700016166 |
| . |
