Algebraic analysis demonstrates the construction of diassociative Q-loops with normal loop rings, indicating a direct link to quaternion subgroups.
A ring R (not necessary associative) is normal with respect to involution σ if xxσ=xσx for every x from R . We construct some class of diassociative loops, named Q -loops, with normal loop rings. By definition a loop L is a Q -loop if every two generated subloop of L is a subgroup of some group H⊆ L isomorphic to quaternion group Q₈ .
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Bovdi et al. (2026) studied this question.
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