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2014 Whitehead graphs and separability in rank two
Matthew Clay, John Conant, Nivetha Ramasubramanian
Involve 7(4): 431-452 (2014). DOI: 10.2140/involve.2014.7.431


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 F2 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 12, where is the number of edges in the graph.


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Matthew Clay. John Conant. Nivetha Ramasubramanian. "Whitehead graphs and separability in rank two." Involve 7 (4) 431 - 452, 2014.


Received: 14 March 2012; Accepted: 27 December 2012; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1305.20033
MathSciNet: MR3239753
Digital Object Identifier: 10.2140/involve.2014.7.431

Primary: 20E05
Secondary: 20F65

Keywords: ‎free groups , primitive elements

Rights: Copyright © 2014 Mathematical Sciences Publishers


Vol.7 • No. 4 • 2014
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