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Whitehead graphs
and separability in rank two
Matt Clay, John Conant and Nivetha Ramasubramanian
Vol. 7 (2014), No. 4, 431–452
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Abstract |
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By applying an algorithm of Stallings regarding separability of elements in a free group, we give an alternative approach to that of Osborne and Zieschang in describing all primitive elements in the free group of rank 2. As a result, we give a proof of a classical result of Nielsen, used by Osborne and Zieschang in their work, that the only automorphisms of that act trivially on the abelianization are those defined by conjugation. Finally, we compute the probability that a Whitehead graph in rank 2 contains a cut vertex. We show that this probability is approximately , where is the number of edges in the graph. |
Keywords
free groups, primitive elements
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Mathematical Subject Classification 2010
Primary: 20E05
Secondary: 20F65
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Milestones
Received: 14 March 2012
Accepted: 27 December 2012
Published: 31 May 2014
Communicated by Gaven Martin
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Authors |
| Matt Clay | |
| Department of Mathematical
Sciences University of Arkansas SCEN 301 Fayetteville, AR 72701 United States |
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| John Conant | |
| Department of Education Shepherd University Shepherdstown, WV 25443 United States |
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| Nivetha Ramasubramanian | |
| Clinton Township, MI 48036 United States |
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