Geodesic
One-relator products of torsion-free groups
Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 99-104

Voir la notice de l'article provenant de la source Cambridge University Press

If A and B are torsion-free groups, and W is a cyclically reduced word of even length in A*B, it is generally conjectured that a Freiheitssatz holds, namely that each of A and B are embedded via the natural map into the one-relator product group G = (A*B)/N(W), where N denotes normal closure. If W has length 2, then G is a free product of A and B with infinite cyclic amalgamation, and the result is obvious. The purpose of this note is to prove the Freiheitssatz in some special cases. 
Brodskiĭ, S. D.; Howie, James. One-relator products of torsion-free groups. Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 99-104. doi: 10.1017/S0017089500009617
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