Abstract. Every quasigroup (loop, Bol loop, group, respectively) is isomorphic to the factor of a subdirectly irreducible quasigroup (loop, Bol loop, group, respectively) over its monolithic congruence.

AMS Subject Classification (1991): 20N05, 08B26

Keyword(s): subdirectly irreducible, quasigroup, loop, wreath product

Received February 15, 2005, and in final form October 17, 2005. (Registered under 5907/2009.)