Vol. 2, No. 2, 2009

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Ordering BS$(1,3)$ using the Magnus transformation

Patrick Bahls, Voula Collins and Elizabeth Heron

Vol. 2 (2009), No. 2, 211–223

Following a similar treatment of the Baumslag–Solitar group BS(1,2) by Bahls, we modify a transformation developed by Magnus to linearly order the group BS(1,3) given by the presentation a,bab = ba3. We demonstrate how this same method will fail to admit such a treatment of the groups BS(1,n), n 4.

Group ordering, BS(1,n), Baumslag–Solitar, Magnus transformation
Mathematical Subject Classification 2000
Primary: 06F15, 20F60
Received: 12 September 2008
Revised: 12 January 2009
Accepted: 13 January 2009
Published: 7 May 2009

Communicated by Nigel Boston
Patrick Bahls
University of North Carolina, Asheville
Asheville, NC 28806
United States
Voula Collins
Department of Mathematics
Wellesley College
Wellesley, MA 02481
United States
Elizabeth Heron
Department of Mathematics
Wake Forest University
Winston-Salem, NC 27109
United States