Construction of Infinite Finitely Presented Nilsemigroup

A. Ya Belov-Kanel; I. A. Ivanov-Pogodaev

doi:10.1134/S1064562420020027

Construction of Infinite Finitely Presented Nilsemigroup

A. Ya Belov-Kanel
, I. A. Ivanov-Pogodaev

Department of Mathematics

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

2 Scopus citations

Abstract

Abstract: An infinite finitely presented nilsemigroup with identity x⁹ = 0 is constructed. This construction answers the question of L.N. Shevrin and M.V. Sapir. The proof is based on the construction of a sequence of geometric complexes, each obtained by gluing several simple 4-cycles (squares). These complexes have certain geometric and combinatorial properties. Actually, the semigroup is the set of word codings of paths on such complexes. Each word codes a path on some complex. Defining relations correspond to pairs of equivalent short paths. The shortest paths in terms of the natural metric are associated with nonzero words in the subgroup. Codings that are not presented by some path or presented by non-shortest paths can be reduced to a zero word.

Original language	English
Pages (from-to)	81-85
Number of pages	5
Journal	Doklady Mathematics
Volume	101
Issue number	2
DOIs	https://doi.org/10.1134/S1064562420020027
State	Published - 1 Mar 2020

Bibliographical note

Publisher Copyright:
© 2020, Pleiades Publishing, Ltd.

Funding

This work was supported by the Russian Science Foundation, grant no. 17-11-01377. The second author is the winner of the contest “Young Russian Mathematics.” ACKNOWLEDGMENTS

Funders	Funder number
Russian Science Foundation	17-11-01377

Keywords

Burnside-type problems
finitely presented semigroups

Access to Document

10.1134/S1064562420020027

Cite this

@article{3f973d774c3c48d68166307cd4db7b1b,

title = "Construction of Infinite Finitely Presented Nilsemigroup",

abstract = "Abstract: An infinite finitely presented nilsemigroup with identity x9 = 0 is constructed. This construction answers the question of L.N. Shevrin and M.V. Sapir. The proof is based on the construction of a sequence of geometric complexes, each obtained by gluing several simple 4-cycles (squares). These complexes have certain geometric and combinatorial properties. Actually, the semigroup is the set of word codings of paths on such complexes. Each word codes a path on some complex. Defining relations correspond to pairs of equivalent short paths. The shortest paths in terms of the natural metric are associated with nonzero words in the subgroup. Codings that are not presented by some path or presented by non-shortest paths can be reduced to a zero word.",

keywords = "Burnside-type problems, finitely presented semigroups",

author = "Belov-Kanel, \{A. Ya\} and Ivanov-Pogodaev, \{I. A.\}",

note = "Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd.",

year = "2020",

month = mar,

day = "1",

doi = "10.1134/S1064562420020027",

language = "אנגלית",

volume = "101",

pages = "81--85",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Pleiades Publishing",

number = "2",

}

TY - JOUR

T1 - Construction of Infinite Finitely Presented Nilsemigroup

AU - Belov-Kanel, A. Ya

AU - Ivanov-Pogodaev, I. A.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - Abstract: An infinite finitely presented nilsemigroup with identity x9 = 0 is constructed. This construction answers the question of L.N. Shevrin and M.V. Sapir. The proof is based on the construction of a sequence of geometric complexes, each obtained by gluing several simple 4-cycles (squares). These complexes have certain geometric and combinatorial properties. Actually, the semigroup is the set of word codings of paths on such complexes. Each word codes a path on some complex. Defining relations correspond to pairs of equivalent short paths. The shortest paths in terms of the natural metric are associated with nonzero words in the subgroup. Codings that are not presented by some path or presented by non-shortest paths can be reduced to a zero word.

AB - Abstract: An infinite finitely presented nilsemigroup with identity x9 = 0 is constructed. This construction answers the question of L.N. Shevrin and M.V. Sapir. The proof is based on the construction of a sequence of geometric complexes, each obtained by gluing several simple 4-cycles (squares). These complexes have certain geometric and combinatorial properties. Actually, the semigroup is the set of word codings of paths on such complexes. Each word codes a path on some complex. Defining relations correspond to pairs of equivalent short paths. The shortest paths in terms of the natural metric are associated with nonzero words in the subgroup. Codings that are not presented by some path or presented by non-shortest paths can be reduced to a zero word.

KW - Burnside-type problems

KW - finitely presented semigroups

UR - https://www.scopus.com/pages/publications/85088165916

U2 - 10.1134/S1064562420020027

DO - 10.1134/S1064562420020027

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85088165916

SN - 1064-5624

VL - 101

SP - 81

EP - 85

JO - Doklady Mathematics

JF - Doklady Mathematics

IS - 2

ER -

Construction of Infinite Finitely Presented Nilsemigroup

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this