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Licensed Unlicensed Requires Authentication Published by De Gruyter March 12, 2009

On loops rich in automorphisms that are abelian modulo the nucleus

Piroska Csörgő and Aleš Drápal
From the journal

Abstract

We prove that a loop Q has to be conjugacy closed modulo Z(Q) whenever all mappings L(x,y) and R(x,y) are automorphisms, N(Q) ⊴ Q, Q/N(Q) is an abelian group, and 〈Lx; xQ〉 is a normal subgroup of the multiplication group.

Received: 2007-03-14
Published Online: 2009-03-12
Published in Print: 2009-May

© de Gruyter 2009