Ends of semigroups

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...

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Bibliographic Details
Published in:Semigroup forum 2016-10, Vol.93 (2), p.330-346
Main Authors: Craik, S., Gray, R., Kilibarda, V., Mitchell, J. D., Ruškuc, N.
Format: Article
Language:English
Subjects:
Algebra
Invariants
Mathematics
Mathematics and Statistics
Research Article
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Summary: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.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-016-9814-9