Can I read The Structure of Automorphic Loops on EtoBox?

The Structure of Automorphic Loops by Kinyon, Michael; Kunen, Ken; Phillips, J. D.; Vojtechovsky, Petr is a scholarly article available to read on EtoBox.

What is The Structure of Automorphic Loops about?

Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes, for instance, groups and commutative Moufang loops. We study uniquely 2-divisible automorphic loops, particularly automorphic loops of odd order, from the point of view of the associated Bruck loops (motivated by Glauberman's work on uniquely 2-divisible Moufang loops) and the associated Lie rings (motivated by a construction of Wright). We prove that every automorphic loop $Q$ of odd order is solvable, contains an element of order $p$ for every prime $p$ dividing $|Q|$, and $|S|$ divides $|Q|$ for every subloop $S$ of $Q$. There are no finite simple nonassociative commutative automorphic loops, and there are no finite simple nonassociative automorphic loops of order less than 2500. We show that if $Q$ is a finite simple nonassociative automorphic loop then the socle of the multiplication group of $Q$ is not regular. The existence of a finite simple nonassociative automorphic loop remains open. Let $p$ be an odd prime. Automorphic loops of order $p$ or $p^2$ are groups, but there exist nonassociative automorphic loops of order $p^3$, some with trivial nucleus (center) and of e

Author

Kinyon, Michael; Kunen, Ken; Phillips, J. D.; Vojtechovsky, Petr

Published

2012

Language

EN