On abelian inner mapping groups of finite loops

Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 4, page 687-691
  • ISSN: 0010-2628

Abstract

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In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.

How to cite

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Niemenmaa, Markku. "On abelian inner mapping groups of finite loops." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 687-691. <http://eudml.org/doc/248617>.

@article{Niemenmaa2000,
abstract = {In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.},
author = {Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; group; connected transversals; finite loops; finite groups; connected transversals; multiplication groups; inner mapping groups},
language = {eng},
number = {4},
pages = {687-691},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On abelian inner mapping groups of finite loops},
url = {http://eudml.org/doc/248617},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Niemenmaa, Markku
TI - On abelian inner mapping groups of finite loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 687
EP - 691
AB - In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.
LA - eng
KW - loop; group; connected transversals; finite loops; finite groups; connected transversals; multiplication groups; inner mapping groups
UR - http://eudml.org/doc/248617
ER -

References

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  2. Drápal A., Kepka T., Alternating groups and latin squares, European J. Combin. 10 (1989), 175-180. (1989) MR0988511
  3. Kepka T., Niemenmaa M., On loops with cyclic inner mapping groups, Arch. Math. 60 (1993), 233-236. (1993) MR1201636
  4. Liebeck M., The classification of the finite simple Moufang loops, Math. Proc. Camb. Phil. Soc. 102 (1987), 33-47. (1987) MR0886433
  5. Niemenmaa M., On the structure of the inner mapping groups of loops, Comm. Algebra 24 (1996), 135-142. (1996) Zbl0853.20049MR1370527
  6. Niemenmaa M., Kepka T., On multiplication groups of loops, J. Algebra 135 (1990), 112-122. (1990) Zbl0706.20046MR1076080
  7. Niemenmaa M., Kepka T., On connected transversals to abelian subgroups, Bull. Austral. Math. Soc. 49 (1994), 121-128. (1994) Zbl0799.20020MR1262682
  8. Rotman J., An introduction to the theory of groups, Springer-Verlag, 1995. Zbl0810.20001MR1307623
  9. Vesanen A., On connected transversals in P S L ( 2 , q ) , Ann. Acad. Sci. Fenn., Series A, I. Mathematica, Dissertationes 84, 1992. Zbl0744.20058MR2714539
  10. Vesanen A., The group P S L ( 2 , q ) is not the multiplication group of a loop, Comm. Algebra 22 (1994), 1177-1195. (1994) MR1261254

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