Semiautomorphic inverse property loops. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Greer, Mark
• Is Part Of: Communications in algebra. Volume 45:Issue 5(2017)
• Page Start: 2222
• Page End: 2237
• Publication Date: 2017-05-04
• Subjects: Moufang loops -- semiautomorphic inverse property loops -- semiautomorphisms -- Steiner loops; 20N05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1233192
• Languages: English
• ISSNs: 0092-7872

Abstract

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.