Completely regular semigroup

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This is a variation of group|Find other variations of group | Read a survey article on varying group
This article defines a semigroup property: a property that can be evaluated to true/false for any given semigroup
View a complete list of semigroup properties


A completely regular semigroup is a semigroup (i.e., a set with associative binary operation) where the subsemigroup generated by any element is a group under the induced multiplication.

Note that the identity elements for these groups need not, in general, coincide. If they do coincide, then the completely regular semigroup is a group.

Relation with other properties

Stronger properties

Weaker properties

Incomparable properties

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