Vv. Benyashkrivets, DECOMPOSING ONE-RELATOR PRODUCTS OF CYCLIC GROUPS INTO FREE-PRODUCTS WITH AMALGAMATION, Sbornik. Mathematics, 189(7-8), 1998, pp. 1125-1137
The problem of the decomposition of one-relator products of cyclics in
to non-trivial free products with amalgamation is considered. Two theo
rems are proved, one of which is as follows. Let G = [a, b \ a(2n) = R
-m(a, b) = 1], where n greater than or equal to 0, m greater than or e
qual to 2, and R(a, b) is a cyclically reduced word containing b in th
e free group on a and b. Then G is a n:on-trivial free product with am
algamation. One consequence of this theorem is a proof of the conjectu
re of Fine, Levin, and Rosenberger that each two-generator one-relator
group with torsion is a non-trivial free product with amalgamation.