Transversals, near transversals, and diagonals in iterated groups and quasigroups

Anna A. Taranenko

Given a binary quasigroup $G$ of order $n$, a $d$-iterated quasigroup $G[d]$ is the $(d+1)$-ary quasigroup equal to the $d$-times composition of $G$ with itself. The Cayley table o…