University of Hertfordshire

By the same authors

Chains of subsemigroups

Research output: Contribution to journalArticlepeer-review

Documents

  • pdf

    Submitted manuscript, 238 KB, PDF document

  • chains_revised

    Accepted author manuscript, 280 KB, PDF document

Links

  • Peter J. Cameron
  • Maximilien Gadouleau
  • James D. Mitchell
  • Yann Peresse
View graph of relations
Original languageEnglish
Pages (from-to)479–508
Number of pages10
JournalIsrael Journal of Mathematics
Volume220
Issue1
Early online date8 May 2017
DOIs
Publication statusPublished - Jun 2017

Abstract

We investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite chains. In some cases, we give lower bounds for the total number of subsemigroups of these semigroups. We give general results for finite completely regular and finite inverse semigroups. Wherever possible, we state our results in the greatest generality; in particular, we include infinite semigroups where the result is true for these. The length of a subgroup chain in a group is bounded by the logarithm of the group order. This fails for semigroups, but it is perhaps surprising that there is a lower bound for the length of a subsemigroup chain in the full transformation semigroup which is a constant multiple of the semigroup order.

ID: 10301041