Finite semigroups that are minimal for not being Malcev nilpotent

Malcev and independently Neumann and Taylor have shown that nilpotent groups can be defined by using semigroup identities, This leads to the notion of a nilpotent semigroup (in the sense of Malcev). In this talk finite semigroups that are close to being nilpotent will be investigated. Obviously every finite semigroup that is not nilpotent has a subsemigroup that is minimal for not being nilpotent, i.e. every proper subsemigroup and every Rees factor semigroup is nilpotent. It is called a minimal non-nilpotent semigroup.