Ends of semigroups

S. Craik, R. Gray, V. Kilibarda, J. Mitchell, N. Ruškuc

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Abstract

We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf’s Theorem, stating that an infinite group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.
Original languageEnglish
Pages (from-to)330-346
Number of pages17
JournalSemigroup Forum
Volume93
Issue number2
Early online date27 Jul 2016
DOIs
Publication statusPublished - Oct 2016

Keywords

  • Digraph
  • Ends
  • Cayley graph

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