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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2017: 0.32

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Friends and relatives of BS(1,2)

Charles F. Miller III
Published Online: 2014-10-09 | DOI: https://doi.org/10.1515/gcc-2014-0006


Algorithms, constructions and examples are of central interest in combinatorial and geometric group theory. Teaching experience and, more recently, preparing a historical essay have led me to think the familiar group BS(1,2) is an example of fundamental importance. The purpose of this note is to make a case for this point of view. We recall several interesting constructions and important examples of groups related to BS(1,2), and indicate why certain of these groups played a key role in showing the word problem for finitely presented groups is unsolvable.

Keywords: Word problem for groups; Baumslag–Solitar groups; Higman's non-hopfian group

MSC: 20F05; 20F10

About the article

Received: 2013-12-19

Published Online: 2014-10-09

Published in Print: 2014-11-01

Citation Information: Groups Complexity Cryptology, Volume 6, Issue 2, Pages 73–80, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2014-0006.

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© 2014 by De Gruyter.Get Permission

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