2 citations · 3 across the 4 of their papers we have counts for
7 papers
Automorphic loops and metabelian groups
Mark Greer, Lee Raney
Given a uniquely 2-divisible group , we study a commutative loop which arises as a result of a construction in \cite{baer}. We investigate some general properties an…
Complete graph decompositions and p-groupoids
John Carr, Mark Greer
We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize P-groupoid…
Simple right conjugacy closed loops
Mark Greer
We give a general construction for right conjugacy closed loops, using for a prime power. Under certain conditions, the loops constructed are simple, giving the first…
Semiautomorphic Inverse Property Loops
Mark Greer
We define a variety of loops called semiautomorphic, inverse property loops that generalize Moufang and Steiner loops. We first show an equivalence between a previously studied var…
Moufang semidirect products of loops with groups and inverse property extensions
Mark Greer, Lee Raney
We investigate Moufang loops which can be written as the semidirect product of a loop and a group. We also examine a particular class of loop extensions which arise as a result of…
A class of loops categorically isomorphic to Bruck loops of odd order
Mark Greer
We define a new variety of loops we call -loops. After showing -loops are power associative, our main goal will be showing a categorical isomorphism between Bruck loops of od…