On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops

Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 2, page 189-193
  • ISSN: 0010-2628

Abstract

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We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group.

How to cite

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Niemenmaa, Markku. "On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops." Commentationes Mathematicae Universitatis Carolinae 59.2 (2018): 189-193. <http://eudml.org/doc/294680>.

@article{Niemenmaa2018,
abstract = {We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group.},
author = {Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; dihedral group; inner mapping group},
language = {eng},
number = {2},
pages = {189-193},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops},
url = {http://eudml.org/doc/294680},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Niemenmaa, Markku
TI - On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 2
SP - 189
EP - 193
AB - We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group.
LA - eng
KW - loop; dihedral group; inner mapping group
UR - http://eudml.org/doc/294680
ER -

References

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  1. Bruck R. H., 10.1090/S0002-9947-1946-0017288-3, Trans. Amer. Math. Soc. 60 (1946), 245–354. Zbl0061.02201MR0017288DOI10.1090/S0002-9947-1946-0017288-3
  2. Drápal A., A class of commutative loops with metacyclic inner mapping groups, Comment. Math. Univ. Carolin. 49 (2008), no. 3, 357–382. MR2490433
  3. Niemenmaa M., 10.1017/S0004972708001093, Bull. Aust. Math. Soc. 79 (2009), no. 1, 109–114. Zbl1167.20039MR2486887DOI10.1017/S0004972708001093
  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. MR2858260
  5. Niemenmaa M., Kepka T., 10.1016/0021-8693(90)90152-E, J. Algebra 135 (1990), no. 1, 112–122. Zbl0706.20046MR1076080DOI10.1016/0021-8693(90)90152-E
  6. Niemenmaa M., Kepka T., 10.1017/S0004972700016166, Bull. Austral. Math. Soc. 49 (1994), no. 1, 121–128. Zbl0799.20020MR1262682DOI10.1017/S0004972700016166

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