Analysis reveals abstract structures of loops with index-two nucleus, suggesting new classification methods.
We study a class of loops admitting an index-two middle nucleus Nμ and an element x∉Nμ satisfying some convenient properties, e.g., x commutes with each element of Nμ. We describe the abstract structure of these loops and solve the relevant isomorphism problem, rendering them amenable to classification. Throughout the article, we highlight various connections to existing theory.
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Louis Rubin (2025) studied this question.
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