On finite loops and their inner mapping groups

Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 341-347
  • ISSN: 0010-2628

Abstract

top
In this paper we consider finite loops and discuss the following problem: Which groups are (are not) isomorphic to inner mapping groups of loops? We recall some known results on this problem and as a new result we show that direct products of dihedral 2-groups and nontrivial cyclic groups of odd order are not isomorphic to inner mapping groups of finite loops.

How to cite

top

Niemenmaa, Markku. "On finite loops and their inner mapping groups." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 341-347. <http://eudml.org/doc/249349>.

@article{Niemenmaa2004,
abstract = {In this paper we consider finite loops and discuss the following problem: Which groups are (are not) isomorphic to inner mapping groups of loops? We recall some known results on this problem and as a new result we show that direct products of dihedral 2-groups and nontrivial cyclic groups of odd order are not isomorphic to inner mapping groups of finite loops.},
author = {Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; group; connected transversals; finite loops; inner mapping groups; connected transversals},
language = {eng},
number = {2},
pages = {341-347},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On finite loops and their inner mapping groups},
url = {http://eudml.org/doc/249349},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Niemenmaa, Markku
TI - On finite loops and their inner mapping groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 341
EP - 347
AB - In this paper we consider finite loops and discuss the following problem: Which groups are (are not) isomorphic to inner mapping groups of loops? We recall some known results on this problem and as a new result we show that direct products of dihedral 2-groups and nontrivial cyclic groups of odd order are not isomorphic to inner mapping groups of finite loops.
LA - eng
KW - loop; group; connected transversals; finite loops; inner mapping groups; connected transversals
UR - http://eudml.org/doc/249349
ER -

References

top
  1. Baer R., Erweiterung von Gruppen und ihren Isomorphismen, Math. Z. 38 (1934), 375-416. (1934) Zbl0009.01101MR1545456
  2. Csörgö P., Myllylä K., Niemenmaa M., On connected transversals to dihedral subgroups of order 2 p n , Algebra Colloquium 7:1 (2000), 105-112. (2000) MR1810601
  3. Drápal A., Orbits of inner mapping groups, Monats. Math. 134 (2002), 191-206. (2002) Zbl1005.20051MR1883500
  4. Huppert B., Endliche Gruppen I, Springer-Verlag, 1967. Zbl0412.20002MR0224703
  5. Kepka T., On the abelian inner permutation groups of loops, Comm. Algebra 26 (1998), 857-861. (1998) Zbl0913.20043MR1606178
  6. Kepka T., Niemenmaa M., On loops with cyclic inner mapping groups, Arch. Math. 60 (1993), 233-236. (1993) MR1201636
  7. Myllylä K., On the solvability of groups and loops, Acta Universitatis Ouluensis, Series A, 396 (2002). 
  8. Niemenmaa M., On loops which have dihedral 2 -groups as inner mapping groups, Bull. Austral. Math. Soc. 52 (1995), 153-160. (1995) Zbl0838.20080MR1344268
  9. Niemenmaa M., On the structure of the inner mapping groups of loops, Comm. Algebra 24 (1996), 135-142. (1996) Zbl0853.20049MR1370527
  10. Niemenmaa M., On finite loops whose inner mapping groups are abelian, Bull. Austral. Math. Soc. 65 (2002), 477-484. (2002) Zbl1012.20068MR1910500
  11. Niemenmaa M., Finite loops with dihedral inner mapping groups are solvable, to appear in J. Algebra. Zbl1047.20051MR2032461
  12. Niemenmaa M., Kepka T., On multiplication groups of loops, J. Algebra 135 (1990), 112-122. (1990) Zbl0706.20046MR1076080
  13. Niemenmaa M., Kepka T., On connected transversals to abelian subgroups, Bull. Austral. Math. Soc. 49 (1994), 121-128. (1994) Zbl0799.20020MR1262682
  14. Vesanen A., On solvable loops and groups, J. Algebra 180 (1996), 862-876. (1996) MR1379214

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.