On non-Hopfian groups of fractions

• Autorzy: Olga Macedońska
• 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.

Słowa kluczowe

EN

Positive law; Hopfian group

Kategorie tematyczne

• 20F05: Generators, relations, and presentations
• 20F99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 398-403

Daty

wydano

2017-01-01

otrzymano

2015-09-28

zaakceptowano

2016-01-11

online

2017-04-20

Twórcy

autor

Olga Macedońska

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice,

Identyfikatory

DOI

10.1515/math-2017-0037