On the construction of regular orthocryptogroups (Q1862911)

Each regular orthocryptogroup is determined by a construction formed from a semilattice \(Y\), a family of rectangular groups \(S_\alpha\) (\(\alpha\in Y\)), a family \(\rho_{\alpha,\beta}\) (\(\alpha\geq\beta\)) of band congruences (on \(S_\alpha\)) and a family \(\psi_{\alpha,\beta}\) of homomorphisms \(S_\alpha\to S_\beta\); a construction which generalizes the concept of a strong semilattice \(Y\) of semigroups \(S_\alpha\). The result is reminiscent of the more general construction in [\textit{M.~Petrich}, Proc. Am. Math. Soc. 99, 617-622 (1987; Zbl 0622.20050)]. All homomorphsims between two regular orthocryptogroups are constructed in terms of their parameters \(Y\), \(S_\alpha\), \(\rho_{\alpha,\beta}\), \(\psi_{\alpha,\beta}\).