TY - JOUR
T1 - Stallings graphs, algebraic extensions and primitive elements in F2
AU - Parzanchevski, Ori
AU - Puder, Doron
N1 - Funding Information:
Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by an Advanced ERC Grant. 07 2014 21 03 2014 157 1 1 11 11 12 2012 Copyright © Cambridge Philosophical Society 2014 2014 Cambridge Philosophical Society
Funding Information:
Supported by an Advanced ERC Grant and the ISF.
PY - 2014/7
Y1 - 2014/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84901695588&partnerID=8YFLogxK
U2 - 10.1017/S0305004114000097
DO - 10.1017/S0305004114000097
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AN - SCOPUS:84901695588
SN - 0305-0041
VL - 157
SP - 1
EP - 11
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 1
ER -