Abstract
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. Let , where , , and is a cyclically reduced word containing in the free group on and . Then 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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