Experimenting with infinite groups, I

Baumslag, G, Cleary, S and Havas, G (2004) Experimenting with infinite groups, I. Experimental Mathematics, 13 4: 495-502.

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Name Description MIMEType Size Downloads
Author Baumslag, G
Cleary, S
Havas, G
Title Experimenting with infinite groups, I
Journal name Experimental Mathematics   Check publisher's open access policy
ISSN 1058-6458
Publication date 2004
Sub-type Article (original research)
Volume 13
Issue 4
Start page 495
End page 502
Total pages 8
Editor R. de la Llave
Place of publication Wellesley
Publisher AK Peters
Collection year 2004
Language eng
Subject C1
280405 Discrete Mathematics
780101 Mathematical sciences
Abstract A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. Since free groups are residually nilpotent, they are parafree. Nonfree parafree groups abound and they all have many properties in common with free groups. Finitely presented parafree groups have solvable word problems, but little is known about the conjugacy and isomorphism problems. The conjugacy problem plays an important part in determining whether an automorphism is inner, which we term the inner automorphism problem. We will attack these and other problems about parafree groups experimentally, in a series of papers, of which this is the first and which is concerned with the isomorphism problem. The approach that we take here is to distinguish some parafree groups by computing the number of epimorphisms onto selected finite groups. It turns out, rather unexpectedly, that an understanding of the quotients of certain groups leads to some new results about equations in free and relatively free groups. We touch on this only lightly here but will discuss this in more depth in a future paper.
Keyword Mathematics
Infinite Groups
Parafree Groups
Finite Quotients
Lower Central Sequence
Relatively Free Group
Isomorphism-problem
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 03:52:09 EST