Explicit constructions of loops with commuting inner mappings

Aleš Drápal; Petr Vojtěchovský

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arXiv · 1509.05706

Explicit constructions of loops with commuting inner mappings

Aleš Drápal·Petr Vojtěchovský

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Abstract

In 2004, Cs\"{o}rg\H{o} constructed a loop of nilpotency class three with abelian group of inner mappings. Until now, no other examples were known. We construct many such loops from groups of nilpotency class two by replacing the product $xy$ with $xyh$ in certain positions, where $h$ is a central involution. The location of the replacements is ultimately governed by a symmetric trilinear alternating form.

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Aleš Drápal, Petr Vojtěchovský. 2015-09-18. Explicit constructions of loops with commuting inner mappings. https://arxiv.org/abs/1509.05706

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