Finitely based finite involution semigroups with non-finitely based reducts

Abstract

Since the study of the nite basis problem for nite semigroups began in the 1960s, it has been unknown if there exists any nite involution semigroup that is nitely based but the reduct of which is non-nitely based. The present article exhibits an example of such an involution semigroup of order n + 5 for any positive integer n.