Accessible Requires Authentication Published by De Gruyter October 9, 2014

Friends and relatives of BS(1,2)

Charles F. Miller III


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.

MSC: 20F05; 20F10
Received: 2013-12-19
Published Online: 2014-10-9
Published in Print: 2014-11-1

© 2014 by De Gruyter