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Mat. Zametki, 2012, Volume 92, Issue 5, Pages 699–706 (Mi mz10128)  

This article is cited in 5 scientific papers (total in 5 papers)

Gröbner–Shirshov Bases for Extended modular, Extended Hecke, and Picard Groups

E. G. Karpuza, A. S. Cevikb

a Karamanoğlu Mehmetbey University
b Selçuk University

Abstract: In this paper, Gröbner–Shirshov bases (noncommutative) for extended modular, extended Hecke and Picard groups are considered. A new algorithm for obtaining normal forms of elements and hence solving the word problem in these groups is proposed.

Keywords: extended modular group, extended Hecke group, Gröbner–Shirshov bases, word problem

DOI: https://doi.org/10.4213/mzm10128

Full text: PDF file (488 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:5, 636–642

Bibliographic databases:

UDC: 512.54
Received: 26.12.2008

Citation: E. G. Karpuz, A. S. Cevik, “Gröbner–Shirshov Bases for Extended modular, Extended Hecke, and Picard Groups”, Mat. Zametki, 92:5 (2012), 699–706; Math. Notes, 92:5 (2012), 636–642

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Karpuz E.G., Ates F., Cevik A.S., Cangul I.N., “The Graph Based on Grobner-Shirshov Bases of Groups”, Fixed Point Theory Appl., 2013 (2013), 71, 14 pp.  crossref  mathscinet  zmath  isi  scopus
    2. L. A. Bokut, Chen Yuqun, “Gröbner-Shirshov bases and their calculation”, Bull. Math. Sci., 4:3 (2014), 325–395  crossref  mathscinet  zmath  isi  scopus
    3. Kangal E., “How effects efficiency on the word problem for monoids?”, Filomat, 30:3 (2016), 733–740  crossref  mathscinet  zmath  isi  scopus
    4. Ates F., Cevik A.S., Guzel Karpuz E., “Grobner-Shirshov Basis For the Singular Part of the Brauer Semigroup”, Turk. J. Math., 42:3 (2018), 1338–1347  crossref  mathscinet  isi  scopus
    5. Birol F., Koruoglu O., Sahin R., Demir B., “Generalized Pell Sequences Related to the Extended Generalized Hecke Groups (H)Over-Bar(3,Q) and An Application to the Group (H)Over-Bar(3,3)”, Honam Math. J., 41:1 (2019), 197–206  crossref  isi
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