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- Title
Stallings graphs, algebraic extensions and primitive elements in F2.
- Authors
PARZANCHEVSKI, ORI; PUDER, DORON
- 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.
- Subjects
GRAPH theory; ALGEBRA; APPLIED mathematics; GROUP extensions (Mathematics); STATISTICS; ALGORITHMS
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2014, Vol 157, Issue 1, p1
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004114000097