Semiautomorphic Inverse Property Loops

2014/03/10 by Mark Greer, Greer, Mark
Mathematics · #20N05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20N05

paper · pdf · doi:10.48550/arxiv.1403.2254

Preprint

arxiv created 2015/02/22 · arxiv updated 2015/02/24

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 a² is a Moufang element, a³ is a c-element and a⁶ 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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