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Stallings graphs, algebraic extensions and primitive elements in F2

Published online by Cambridge University Press:  21 March 2014

ORI PARZANCHEVSKI  and
DORON PUDER
ORI PARZANCHEVSKI
Affiliation:
Einstein Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel. e-mails: parzan@math.huji.ac.il, doronpuder@gmail.com
DORON PUDER
Affiliation:
Einstein Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel. e-mails: parzan@math.huji.ac.il, doronpuder@gmail.com
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Abstract

We study the free group of rank two from the point of view of Stallings core graphs. The first half of the paper examines primitive elements in this group, giving new and self-contained proofs for various known results about them. In particular, this includes the classification of bases of this group. The second half of the paper is devoted to constructing a counterexample to a conjecture by Miasnikov, Ventura and Weil, which seeks to characterize algebraic extensions in free groups in terms of Stallings graphs.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 1 , July 2014 , pp. 1 - 11
Copyright
Copyright © Cambridge Philosophical Society 2014 

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References

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