The notion of Abelian Kernel of a finite monoid extends the notion of
derived subgroup of a finite group. In this line, an extension of the
notion of solvable group to idempotent commuting monoids is quite
natural: the solvable monoids are the monoids such that the chain
of iterated Abelian kernels ends with the set of idempotents. We prove
that the finite idempotent commuting monoids satisfying this property
are precisely those whose subgroups are solvable.
Sponsored in part by the FCT approved projects POCTI 32817/99 and POCTI/MAT/37670/2001 in participation with the European Community Fund FEDER and by FCT through Centro de Matemática da Universidade do Porto. Also sponsored in part by FCT, the Faculdade de Ciências da Universidade do Porto, Programa Operacional Ciência, Tecnologia, Inovação do Quadro Comunitário de Apoio III, and by Caixa Geral de Depósitos.