Conjugacy in Semigroups
نویسندگان
چکیده
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, which can be applied to an arbitrary semigroup, including semigroups with zero. We characterize this conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups in the case when the set is infinite. 2010 Mathematics Subject Classification. 20M20.
منابع مشابه
Conjugation in Semigroups
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 comp...
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