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math.GR2010
Powers of Elements in Jordan Loops
Kyle Pula
A Jordan loop is a commutative loop satisfying the Jordan identity . We establish several identities involving powers in Jordan loops and show that there is…
math.CO2010
Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjecture
Kyle Pula
For a finite loop , let be the set of elements that can be represented as a product containing each element of precisely once. Motivated by the recent proof of the H…
math.CO2010★ 2 cited
A Generalization of Plexes of Latin Squares
Kyle Pula
A -plex of a latin square is a collection of cells representing each row, column, and symbol precisely times. The classic case of is more commonly known as a transvers…