On the solvability of commutative loops and their multiplication groups

Kari Myllylä; Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 209-213
  • ISSN: 0010-2628

Abstract

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We investigate the situation when the inner mapping group of a commutative loop is of order 2 p , where p = 4 t + 3 is a prime number, and we show that then the loop is solvable.

How to cite

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Myllylä, Kari, and Niemenmaa, Markku. "On the solvability of commutative loops and their multiplication groups." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 209-213. <http://eudml.org/doc/248436>.

@article{Myllylä1999,
abstract = {We investigate the situation when the inner mapping group of a commutative loop is of order $2p$, where $p=4t+3$ is a prime number, and we show that then the loop is solvable.},
author = {Myllylä, Kari, Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {solvability; loop; group; solvability of finite groups; solvability of finite loops; finite commutative loops; inner mapping groups},
language = {eng},
number = {2},
pages = {209-213},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the solvability of commutative loops and their multiplication groups},
url = {http://eudml.org/doc/248436},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Myllylä, Kari
AU - Niemenmaa, Markku
TI - On the solvability of commutative loops and their multiplication groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 209
EP - 213
AB - We investigate the situation when the inner mapping group of a commutative loop is of order $2p$, where $p=4t+3$ is a prime number, and we show that then the loop is solvable.
LA - eng
KW - solvability; loop; group; solvability of finite groups; solvability of finite loops; finite commutative loops; inner mapping groups
UR - http://eudml.org/doc/248436
ER -

References

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  1. Bruck R.H., Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245-354. (1946) Zbl0061.02201MR0017288
  2. Gorenstein D., Finite Groups, Harper & Row, New York, 1968. Zbl0695.20014MR0231903
  3. Herstein I.N., A remark on finite groups, Proc. Amer. Math. Soc. 9 (1958), 255-257. (1958) Zbl0089.01601MR0093542
  4. Neumann P.M., Stoy G., Thompson E., Groups and Ggeometry, Oxford University Press, 1994. MR1283590
  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., On loops which have dihedral 2 -groups as inner mapping groups, Bull. Australian Math. Soc. 52 (1995), 153-160. (1995) Zbl0838.20080MR1344268
  7. Niemenmaa M., On connected transversals to subgroups whose order is a product of two primes, European J. Comb. 18 (1997), 915-919. (1997) Zbl0889.20044MR1485376
  8. Niemenmaa M., Kepka T., On multiplication groups of loops, J. Algebra 135 (1990), 112-122. (1990) Zbl0706.20046MR1076080
  9. Niemenmaa M., Kepka T., On connected transversals to abelian subgroups, Bull. Australian Math. Soc. 49 (1994), 121-128. (1994) Zbl0799.20020MR1262682
  10. Niemenmaa M., Vesanen A., On subgroups, transversals and commutators, in Proceeding of the Groups Galway/St. Andrews 1993, London Math. Soc. Lecture Notes Series 212 (1995), pp.476-481. Zbl0862.20023MR1337289
  11. Vesanen A., Solvable groups and loops, J. Algebra 180 (1996), 862-876. (1996) Zbl0853.20050MR1379214

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