39 citations · 76 across the 8 of their papers we have counts for
12 papers · 1 filter
Loops of Bol-Moufang type with a subgroup of index two
Michael K. Kinyon, J. D. Phillips, Petr Vojtěchovský
We describe all constructions for loops of Bol-Moufang type analogous to the Chein construction for Moufang loops.
Rectangular loops and rectangular quasigroups
Michael K. Kinyon, J. D. Phillips
We solve two problems posed by Krapež by finding a basis of seven independent axioms for the variety of rectangular loops. Six of these axioms form a basis for the variety of recta…
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)…
Infinite Simple Bol Loops
Hubert Kiechle, Michael K. Kinyon
If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.
Axioms for trimedial quasigroups
Michael K. Kinyon, J. D. Phillips
We give new equations that axiomatize the variety of trimedial quasigroups. We also improve a standard characterization by showing that right semimedial, left F-quasigroups are tri…
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…