GB-problem in the class of locally graded groups

O. Macedonska; Piotr Slanina

doi:10.1080/00927870701776599

GB-problem in the class of locally graded groups

O. Macedonska
, Piotr Slanina

Department of Mathematics (RMS/RMS1)

Silesian University of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

A problem, we consider, is equivalent to the one posed in 1981 by Bergman: Let G be a group and S a subsemigroup of G which generates G as a group. Must each identity satisfied in S be satisfied in G? The first counterexample was found in 2005 by Ivanov and Storozhev. It gives a negative answer to the problem in general. However we show that the problem has an affirmative answer for locally residually finite groups and for locally graded groups containing no free noncyclic subsemigroups.

Original language	English
Pages (from-to)	842-850
Number of pages	9
Journal	Communications in Algebra
Volume	36
Issue number	3
DOIs	https://doi.org/10.1080/00927870701776599
Publication status	Published - Mar 2008

Keywords

Generating subsemigroup in a group
Semigroup identities

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1080/00927870701776599

Cite this

@article{a52f0399cac14133b8ac669edaed5afb,

title = "GB-problem in the class of locally graded groups",

abstract = "A problem, we consider, is equivalent to the one posed in 1981 by Bergman: Let G be a group and S a subsemigroup of G which generates G as a group. Must each identity satisfied in S be satisfied in G? The first counterexample was found in 2005 by Ivanov and Storozhev. It gives a negative answer to the problem in general. However we show that the problem has an affirmative answer for locally residually finite groups and for locally graded groups containing no free noncyclic subsemigroups.",

keywords = "Generating subsemigroup in a group, Semigroup identities",

author = "O. Macedonska and Piotr Slanina",

year = "2008",

month = mar,

doi = "10.1080/00927870701776599",

language = "English",

volume = "36",

pages = "842--850",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "3",

}

TY - JOUR

T1 - GB-problem in the class of locally graded groups

AU - Macedonska, O.

AU - Slanina, Piotr

PY - 2008/3

Y1 - 2008/3

N2 - A problem, we consider, is equivalent to the one posed in 1981 by Bergman: Let G be a group and S a subsemigroup of G which generates G as a group. Must each identity satisfied in S be satisfied in G? The first counterexample was found in 2005 by Ivanov and Storozhev. It gives a negative answer to the problem in general. However we show that the problem has an affirmative answer for locally residually finite groups and for locally graded groups containing no free noncyclic subsemigroups.

AB - A problem, we consider, is equivalent to the one posed in 1981 by Bergman: Let G be a group and S a subsemigroup of G which generates G as a group. Must each identity satisfied in S be satisfied in G? The first counterexample was found in 2005 by Ivanov and Storozhev. It gives a negative answer to the problem in general. However we show that the problem has an affirmative answer for locally residually finite groups and for locally graded groups containing no free noncyclic subsemigroups.

KW - Generating subsemigroup in a group

KW - Semigroup identities

UR - https://www.scopus.com/pages/publications/45849103565

U2 - 10.1080/00927870701776599

DO - 10.1080/00927870701776599

M3 - Article

AN - SCOPUS:45849103565

SN - 0092-7872

VL - 36

SP - 842

EP - 850

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

ER -

GB-problem in the class of locally graded groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this