Conjugation in Semigroups
arXiv:1301.1568 · doi:10.1016/j.jalgebra.2013.12.025
Abstract
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.
41 pages, 14 figures
References in corpus (2)
Cited by in corpus (6)
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- Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids
- Deciding conjugacy in sylvester monoids and other homogeneous monoids
- Conjugacy and Least Commutative Congruences in Semigroups
- On the complexity of inverse semigroup conjugacy
- Conjugacy in Patience Sorting monoids