Infinite simple Bol loops

Hubert Kiechle; Michael K. Kinyon

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 275-278
  • ISSN: 0010-2628

Abstract

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If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.

How to cite

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Kiechle, Hubert, and Kinyon, Michael K.. "Infinite simple Bol loops." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 275-278. <http://eudml.org/doc/249352>.

@article{Kiechle2004,
abstract = {If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.},
author = {Kiechle, Hubert, Kinyon, Michael K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Bol loop; K-loop; Bruck loop; Bol loops; K-loops; Bruck loops},
language = {eng},
number = {2},
pages = {275-278},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Infinite simple Bol loops},
url = {http://eudml.org/doc/249352},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Kiechle, Hubert
AU - Kinyon, Michael K.
TI - Infinite simple Bol loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 275
EP - 278
AB - If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.
LA - eng
KW - Bol loop; K-loop; Bruck loop; Bol loops; K-loops; Bruck loops
UR - http://eudml.org/doc/249352
ER -

References

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  1. Aschbacher M., Kinyon M.K., Phillips J.D., Finite Bruck loops, submitted. Available at http://www.arXiv.org/abs/math.GR/0401193. Zbl1102.20046
  2. Bruck R.H., A Survey of Binary Systems, Springer-Verlag, Berlin-Heidelberg-New York, 1971; MR 20{#}76, Zbl. 206:30301. Zbl0141.01401MR0093552
  3. Foguel T., Ungar A.A., Gyrogroups and the decomposition of groups into twisted subgroups and subgroups, Pacific J. Math. 197 (2001), 1-11; MR 2002e:20142, Zbl. pre01589578. (2001) Zbl1066.20068MR1810204
  4. Huppert B., Endliche Gruppen I, Springer-Verlag, Berlin-Heidelberg-New York, 1967; MR 37 {#}302, Zbl. 0217.07201. Zbl0412.20002MR0224703
  5. Kiechle H., Theory of K-loops, Lecture Notes in Math. 1778, Springer-Verlag, Berlin-Heidelberg-New York, 2002; MR 2003d:20109, Zbl. 0997.20059. Zbl0997.20059MR1899153
  6. Nagy P.T., Strambach K., Loops in Group Theory and Lie Theory, de Gruyter Expositions in Mathematics 35, Walter de Gruyter, Berlin-New York, 2003; MR 2003d:20110, Zbl. pre01732502. Zbl1050.22001MR1899331
  7. Rózga K., On central extensions of gyrocommutative gyrogroups, Pacific J. Math. 193 (2000), 201-218; MR 2001a:20115, Zbl. 1010.20055. (2000) MR1748188
  8. Scott W.R., Group Theory, Dover, New York, 1987; MR 88d:20001, Zbl. 0641.20001. Zbl0897.20029MR0896269

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