On finite loops whose inner mapping groups have small orders

Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 3, page 651-654
  • ISSN: 0010-2628

Abstract

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We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.

How to cite

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Niemenmaa, Markku. "On finite loops whose inner mapping groups have small orders." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 651-654. <http://eudml.org/doc/247908>.

@article{Niemenmaa1996,
abstract = {We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.},
author = {Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {solvability; loop; group; solvability; finite loops; finite groups; left transversal; left translations; multiplication groups; inner mapping groups},
language = {eng},
number = {3},
pages = {651-654},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On finite loops whose inner mapping groups have small orders},
url = {http://eudml.org/doc/247908},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Niemenmaa, Markku
TI - On finite loops whose inner mapping groups have small orders
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 651
EP - 654
AB - We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.
LA - eng
KW - solvability; loop; group; solvability; finite loops; finite groups; left transversal; left translations; multiplication groups; inner mapping groups
UR - http://eudml.org/doc/247908
ER -

References

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  1. Blackburn N., Huppert B., Finite Groups III, Springer Verlag, 1982. Zbl0514.20002MR0662826
  2. Conway J.H., Atlas of Finite Groups, Oxford, Clarendon Press, 1985. Zbl0568.20001MR0827219
  3. Huppert B., Endliche Gruppen I, Springer Verlag, 1967. Zbl0412.20002MR0224703
  4. Kepka T., Niemenmaa M., On loops with cyclic inner mapping groups, Arch. Math. 60 (1993), 233-236. (1993) MR1201636
  5. Niemenmaa M., Transversals, commutators and solvability in finite groups, Bollettino U.M.I. (7) 9-A (1995), 203-208. (1995) Zbl0837.20026MR1324621
  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 in finite groups, Bull. London Math. Soc. 24 (1992), 343-346. (1992) Zbl0793.20064MR1165376
  8. Niemenmaa M., Vesanen A., On subgroups, transversals and commutators, Groups Galway/St. Andrews, 1993, Vol.2, London Math. Soc. Lecture Notes Series 212, 1995, pp. 476-481. Zbl0862.20023MR1337289
  9. Vesanen A., On connected transversals in P S L ( 2 , q ) , Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 84, 1992. Zbl0744.20058MR1150782
  10. Vesanen A., The group P S L ( 2 , q ) is not the multiplication group of a loop, Comm. Algebra 22.4 (1994), 1177-1195. (1994) MR1261254
  11. Vesanen A., Solvable loops and groups, to appear in J. Algebra. MR1379214

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