Presentations of inverse semigroups, their kernels and extensions

C.A. Carvalho, R Gray, Nik Ruskuc

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K. We show how to obtain a presentation for K from a presentation for S, and vice versa. We then investigate the relationship between the properties of S, K and T, focusing mainly on finiteness conditions. In particular we consider finite presentability, solubility of the word problem, residual finiteness, and the homological finiteness property FPn. Our results extend several classical results from combinatorial group theory concerning group extensions to inverse semigroups. Examples are also provided that highlight the differences with the special case of groups.
Original languageEnglish
Pages (from-to)289-316
JournalJournal of the Australian Mathematical Society
Issue number3
Publication statusPublished - 1 Jun 2011


  • Inverse semigroup presentations
  • Reidemeister-Schreier
  • Kernel
  • Finiteness conditions


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