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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