Quasigroup Words and Reversible Automata

This paper examines two related topics: the linearization of the reversible automata of Gvaramiya and Plotkin, and the problem of finding a faithful representation of the words in a central quasigroup that respects the triality symmetry of the language of quasigroups. In particular, it is shown that every central pique is a module over a ring on which the triality group acts.