1998
DOI: 10.1007/pl00005944
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Semigroups with the Congruence Extension Property

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Cited by 11 publications
(10 citation statements)
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“…In this case the CEP is equivalent to the assertion that the element represented by w has order n in the one relator group F/ w n F , which is a part of the well known theorem of Karrass, Magnus, and Solitar [10]. The CEP has been extensively studied for groups, semigroups, and universal algebras (see [1,21,25] and references therein). It also plays an important role in some constructions of groups with 'exotic' properties (see for instance [16]).…”
Section: Introductionmentioning
confidence: 99%
“…In this case the CEP is equivalent to the assertion that the element represented by w has order n in the one relator group F/ w n F , which is a part of the well known theorem of Karrass, Magnus, and Solitar [10]. The CEP has been extensively studied for groups, semigroups, and universal algebras (see [1,21,25] and references therein). It also plays an important role in some constructions of groups with 'exotic' properties (see for instance [16]).…”
Section: Introductionmentioning
confidence: 99%
“…(xi) If a ∈ Q α , b ∈ Q β , and α β > αβ, then ax = a ⇔ bx = b and xa = a ⇔ xb = b for any x ∈ S. Theorem 1.8 [13]. A semigroup S has CEP if and only if S satisfies the CEP conditions.…”
Section: Lemma 14 [2] the Following Conditions On A Semigroup S Arementioning
confidence: 97%
“…So S α = I α × G α × α ∪ Q α is a nil extension of a rectangular group (see [13], [15]). Throughout this paper, we denote a semigroup S which is a semilattice of nil extensions of rectangular groups by the form as above.…”
Section: Lemma 14 [2] the Following Conditions On A Semigroup S Arementioning
confidence: 98%
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“…This easily implies the Higman-Neumann-Neumann theorem stating that any countable group can be embedded into a 2-generated group. The CEP has also been extensively studied for semigroups and universal algebras (see [3,33,37] and references therein). It plays an important role in some constructions of groups with "exotic" properties [23].…”
Section: Corollary 22 There Is a Finite Subset Of Nontrivial Elementsmentioning
confidence: 99%