Decomposing one-relator products of cyclic groups into free products with amalgamation

V. V. Benyash-Krivets

Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1125-1137

Résumé

The problem of the decomposition of one-relator products of cyclics into non-trivial free products with amalgamation is considered. Two theorems are proved, one of which is as follows. \textit{ Let $G=\langle a,b\mid a^{2n}=R^m(a,b)=1\rangle $, where $n\geqslant 0$, $m\geqslant 2$, and $R(a,b)$ is a cyclically reduced word containing $b$ in the free group on $a$ and $b$. Then $G$ is a non-trivial free product with amalgamation.} One consequence of this theorem is a proof of the conjecture of Fine, Levin, and Rosenberger that each two-generator one-relator group with torsion is a non-trivial free product with amalgamation.