Geodesic
Decomposing one-relator products of cyclic groups into free products with amalgamation
Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1125-1137 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Decomposing one-relator products of cyclic groups into free products with amalgamation},
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V. V. Benyash-Krivets. Decomposing one-relator products of cyclic groups into free products with amalgamation. Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1125-1137. http://geodesic.mathdoc.fr/item/SM_1998_189_8_a1/

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