Conjugation in semigroups

Araújo, João; Konieczny, Janusz; Malheiro, António

http://hdl.handle.net/10400.2/3798

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Authors

Araújo, João

Konieczny, Janusz

Malheiro, António

Abstract(s)

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.

Keywords

Semigroups Conjugacy Transformations Directed graphs Well-founded relations

URI

http://hdl.handle.net/10400.2/3798

Citation

Araújo, João; Konieczny, Janusz; Malheiro, António - Conjugation in semigroups. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 403 (2014), p. 1-34