• DOI:10.1090/S0002-9947-1982-0654843-3
• Corpus ID: 119482339

Nilpotent inverse semigroups with central idempotents

@article{Kowol1982NilpotentIS,
  title={Nilpotent inverse semigroups with central idempotents},
  author={Gerhard Kowol and Heinz Mitsch},
  journal={Transactions of the American Mathematical Society},
  year={1982},
  volume={271},
  pages={437-449}
}

• G. Kowol, H. Mitsch
• Published 1 February 1982
• Mathematics
• Transactions of the American Mathematical Society

An inverse semigroup S with central idempotents, i.e. a strong semilattice of groups, will be called nilpotent, if it is finite and if for each prime divisor p¡ of the orders of the structure groups of S the sets P¡ = {s G S\ o(s) = pf", ks > 0} are subsemigroups of S. If 5 is a group, then P¡ are exactly the Sylow />,-subgroups of the group. A theory similar to that given by W. Burnside for finite nilpotcnt groups is developed introducing the concepts of ascending resp. descending central series in an inverse semigroup, and it is shown that almost all of the well-known properties of finite nilpotent groups do hold also for the class of finite inverse semigroups with central idempotents.