# 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

top## How 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 ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.