A graph-theoretic proof for Whitehead's second free-group algorithm
J.H.C. Whitehead's second free-group algorithm determines whether or not two given elements of a free group lie in the same orbit of the automorphism group of the free group. The algorithm involves certain connected graphs, and Whitehead used three-manifold models to prove their connectedness;...
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| creator | Dicks, Warren |
| description | J.H.C. Whitehead's second free-group algorithm determines whether or not two
given elements of a free group lie in the same orbit of the automorphism group
of the free group. The algorithm involves certain connected graphs, and
Whitehead used three-manifold models to prove their connectedness; later,
Rapaport and Higgins & Lyndon gave group-theoretic proofs. Combined work of
Gersten, Stallings, and Hoare showed that the three-manifold models may be
viewed as graphs. We give the direct translation of Whitehead's topological
argument into the language of graph theory. |
| doi_str_mv | 10.48550/arxiv.1706.09679 |
| format | Article |
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given elements of a free group lie in the same orbit of the automorphism group
of the free group. The algorithm involves certain connected graphs, and
Whitehead used three-manifold models to prove their connectedness; later,
Rapaport and Higgins & Lyndon gave group-theoretic proofs. Combined work of
Gersten, Stallings, and Hoare showed that the three-manifold models may be
viewed as graphs. We give the direct translation of Whitehead's topological
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given elements of a free group lie in the same orbit of the automorphism group
of the free group. The algorithm involves certain connected graphs, and
Whitehead used three-manifold models to prove their connectedness; later,
Rapaport and Higgins & Lyndon gave group-theoretic proofs. Combined work of
Gersten, Stallings, and Hoare showed that the three-manifold models may be
viewed as graphs. We give the direct translation of Whitehead's topological
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given elements of a free group lie in the same orbit of the automorphism group
of the free group. The algorithm involves certain connected graphs, and
Whitehead used three-manifold models to prove their connectedness; later,
Rapaport and Higgins & Lyndon gave group-theoretic proofs. Combined work of
Gersten, Stallings, and Hoare showed that the three-manifold models may be
viewed as graphs. We give the direct translation of Whitehead's topological
argument into the language of graph theory.</abstract><doi>10.48550/arxiv.1706.09679</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Group Theory |
| title | A graph-theoretic proof for Whitehead's second free-group algorithm |
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