53 citations · 351 across the 79 of their papers we have counts for
6 papers · 1 filter
C-loops: extensions and constructions
Michael K. Kinyon, J. D. Phillips, Petr Vojtěchovský
C-loops are loops satisfying the identity . We develop the theory of extensions of C-loops, and characterize all nuclear extensions provided the nucleu…
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.
Leibniz algebras, Lie racks, and digroups
Michael K. Kinyon
The "coquecigrue" problem for Leibniz algebras is that of finding an appropriate generalization of Lie's third theorem, that is, of finding a generalization of the notion of group…
Finite Bruck Loops
Michael Aschbacher, Michael K. Kinyon, J. D. Phillips
A loop is said to be a Bruck loop if it satisfies the (right) Bol identity and the automorphic inverse propert…