The Semigroup Efficiency of Groups and Monoids
نویسنده
چکیده
A nite semigroup (respectively monoid or group) S is said to be eecient if it can be deened by a semigroup (respectively monoid or group) presentation hA jRi with jRj ? jAj = rank(H 2 (S 1)). In this paper we show that a group is eecient as a group if and only if it is eecient as a monoid, but some eecient monoids are not eecient as semigroups. Moreover we show that certain classes of eecient groups are eecient as semigroups.
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