39 citations · 59 across the 11 of their papers we have counts for
4 papers · 1 filter
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…
Every diassociative A-loop is Moufang
Michael K. Kinyon, Kenneth Kunen, J. D. Phillips
An A-loop is a loop in which every inner mapping is an automorphism. We settle a problem which had been open since 1956 by showing that every diassociative A-loop is Moufang.