A-loops close to code loops are groups

Aleš Drápal

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 2, page 245-249
  • ISSN: 0010-2628

Abstract

top
Let be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group.

How to cite

top

Drápal, Aleš. "A-loops close to code loops are groups." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 245-249. <http://eudml.org/doc/248618>.

@article{Drápal2000,
abstract = {Let $Q$ be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group.},
author = {Drápal, Aleš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {A-loop; central nilpotency; Osborn problem; central nilpotency; Osborn problem; diassociative A-loop; right translations; central subloop; code loops; Moufang loop},
language = {eng},
number = {2},
pages = {245-249},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A-loops close to code loops are groups},
url = {http://eudml.org/doc/248618},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Drápal, Aleš
TI - A-loops close to code loops are groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 245
EP - 249
AB - Let $Q$ be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group.
LA - eng
KW - A-loop; central nilpotency; Osborn problem; central nilpotency; Osborn problem; diassociative A-loop; right translations; central subloop; code loops; Moufang loop
UR - http://eudml.org/doc/248618
ER -

References

top
  1. Aschbacher M., Sporadic Groups, Cambridge Tracts in Mathematics 104, Cambridge University Press, 1994. Zbl0804.20011MR1269103
  2. Bruck R.H., Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245-354. (1946) Zbl0061.02201MR0017288
  3. Bruck R.H., Paige L.J., Loops whose inner mappings are automorphisms, Ann. of Math. 63 (1954), 308-323. (1954) MR0076779
  4. Chein O., Goodaire E.G., Moufang loops with a unique non-identity commutator (associator, square), J. Algebra 130 (1990), 369-384. (1990) MR1051308
  5. Griess R.L., Jr., Code loops, J. Algebra 100 (1986), 224-234. (1986) Zbl0589.20051MR0839580
  6. Osborn M.J., A theorem on A-loops, Proc. Amer. Math. Soc. 9 (1958), 347-349. (1958) Zbl0097.25302MR0093555
  7. Phillips J.D., On Moufang A-loops, Comment. Math. Univ. Carolinae 41 (2000), 371-375. (2000) Zbl1038.20050MR1780878

NotesEmbed ?

top

You must be logged in to post comments.