Finitely based finite involution semigroups with non-finitely based reducts

Abstract

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