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Open Mathematics

2017 | 15 | 1 | 398-403
Tytuł artykułu

On non-Hopfian groups of fractions

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Języki publikacji
EN
Abstrakty
EN
The group of fractions of a semigroup S, if exists, can be written as G = SS−1. If S is abelian, then G must be abelian. We say that a semigroup identity is transferable if being satisfied in S it must be satisfied in G = SS−1. One of problems posed by G.Bergman in 1981 asks whether the group G must satisfy every semigroup identity which is satisfied in S, that is whether every semigroup identity is transferable. The first non-transferable identities were constructed in 2005 by S.V.Ivanov and A.M. Storozhev. A group G is called Hopfian if each epimorphizm G → G is the automorphism. The residually finite groups are Hopfian, however there are many problems concerning the Hopfian property e.g. of infinite Burnside groups, of finitely generated relatively free groups [11, Problem 15]. We prove here that if G = SS−1 is an n-generator group of fractions of a relatively free semigroup S, satisfying m-variable (m < n) non-transferable identity, then G is the non-Hopfian group.
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EN
Kategorie tematyczne
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Tom
Numer
Strony
398-403
Opis fizyczny
Daty
wydano
2017-01-01
otrzymano
2015-09-28
zaakceptowano
2016-01-11
online
2017-04-20
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