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Semiautomorphic Inverse Property Loops

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Preprint
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arXiv ID: 1403.2254
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arXiv
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Abstract

We define a variety of loops called semiautomorphic, inverse property loops that generalize Moufang and Steiner loops. We first show an equivalence between a previously studied variety of loops. Next we extend several known results for Moufang and Steiner loops. That is, the commutant is a subloop and if $a$ is in the commutant, then $a^{2}$ is a Moufang element, $a^{3}$ is a $c$-element and $a^{6}$ is in the center. Finally, we give two constructions for semiautomorphic inverse property loops based on Chein's and de Barros and Juriaans' doubling constructions.

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