39 citations · 83 across the 30 of their papers we have counts for
7 papers · 1 filter
Loops with universal and semi-universal flexibility
Riley Britten, Michael Kinyon, Kenneth Kunen +1
We study loops which are universal (that is, isotopically invariant) with respect to the property of flexibility (). We also weaken this to semi-universality…
The structure of automorphic loops
Michael Kinyon, Ken Kunen, J. D. Phillips +1
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-d…
Power-associative, conjugacy closed loops
Michael K. Kinyon, Kenneth Kunen
We study conjugacy closed loops (CC-loops) and power-associative CC-loops (PACC-loops). If is a PACC-loop with nucleus , then is an abelian group of exponent 12; if in…
The structure of extra loops
Michael K. Kinyon, Kenneth Kunen
The Sylow theorems hold for finite extra loops, as does P. Hall's theorem for finite solvable extra loops. Every finite nonassociative extra loop has a nontrivial center, $Z(Q)…
Diassociativity in Conjugacy Closed Loops
Michael K. Kinyon, Kenneth Kunen, J. D. Phillips
Let be a conjugacy closed loop, and its nucleus. Then contains all associators of elements of . If in addition is diassociative (i.e., an extra loop), t…
A Generalization of Moufang and Steiner Loops
Michael K. Kinyon, Kenneth Kunen, J. D. Phillips
We study a variety of loops, RIF, which arise naturally from considering inner mapping groups, and a somewhat larger variety, ARIF. All Steiner and Moufang loops are RIF, and all f…