A-loops close to code loops are groups
Commentationes Mathematicae Universitatis Carolinae (2000)
- Volume: 41, Issue: 2, page 245-249
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topDrápal, 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- Aschbacher M., Sporadic Groups, Cambridge Tracts in Mathematics 104, Cambridge University Press, 1994. Zbl0804.20011MR1269103
- Bruck R.H., Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245-354. (1946) Zbl0061.02201MR0017288
- Bruck R.H., Paige L.J., Loops whose inner mappings are automorphisms, Ann. of Math. 63 (1954), 308-323. (1954) MR0076779
- Chein O., Goodaire E.G., Moufang loops with a unique non-identity commutator (associator, square), J. Algebra 130 (1990), 369-384. (1990) MR1051308
- Griess R.L., Jr., Code loops, J. Algebra 100 (1986), 224-234. (1986) Zbl0589.20051MR0839580
- Osborn M.J., A theorem on A-loops, Proc. Amer. Math. Soc. 9 (1958), 347-349. (1958) Zbl0097.25302MR0093555
- Phillips J.D., On Moufang A-loops, Comment. Math. Univ. Carolinae 41 (2000), 371-375. (2000) Zbl1038.20050MR1780878
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.