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.
@article{119160,
author = {Ale\v s Dr\'apal},
title = {A-loops close to code loops are groups},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {41},
year = {2000},
pages = {245-249},
zbl = {1038.20046},
mrnumber = {1780868},
language = {en},
url = {http://dml.mathdoc.fr/item/119160}
}
Drápal, Aleš. A-loops close to code loops are groups. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 245-249. http://gdmltest.u-ga.fr/item/119160/
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