This article is cited in 1 paper

Automorphisms of Commutative Moufang Loops Satisfying the Minimality Condition

N. T. Lupasço, N. I. Sandu

Tiraspol State University

Abstract: We consider commutative Moufang loops $Q$ with multiplicative group $\mathfrak{M}$ satisfying the minimality condition for its subloops. Such loops, as well as the class of such loops, are characterized by various subgroups of automorphism groups $\operatorname{Aut}Q$ and $\operatorname{Aut}\mathfrak{M}$. We study the structure of the groups $\operatorname{Aut}Q$ and $\operatorname{Aut}\mathfrak{M}$ and prove that these groups have matrix representations.

Keywords: commutative Moufang loop, automorphism group, Abelian group, subloop, associator, quasicyclic group, multiplicative group.

Received: 03.10.2005
Revised: 04.10.2010

DOI: 10.4213/mzm4413

 English version: Mathematical Notes, 2012, 91:3, 384–398

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