On Free Products of Completely Regular Semigroups
نویسنده
چکیده
The free product CR S i of an arbitrary family of disjoint completely simple semigroups fS i g i2I , within the variety CR of completely regular semigroups, is described by means of a theorem generalizing that of Ka dourek and Poll ak for free completely regular semigroups. A notable consequence of the description is that all maximal subgroups of CR S i are free, except for those in the factors S i themselves. The general theorem simpliies in the case of free CR-products of groups and, in particular, free idempotent-generated completely regular semigroups. dourek and L. Poll ak 8] have ooered solutions to the word problem for the free completely regular semigroup FCR X on a countably innnite set X. This semigroup is clearly the free product, in the variety CR of completely regular semigroups, of a family of innnite cyclic groups. We prove (Theorem 4.1) that, suitably modiied, the method of Ka dourek and Poll ak serves to solve the word problem in the free CR-product of any family of disjoint completely simple semigroups (modulo eeective description of 1
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