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This article is cited in 2 scientific papers (total in 2 papers)
Decomposing one-relator products of cyclic groups into free products with amalgamation
V. V. Benyash-Krivets Institute of Mathematics, National Academy of Sciences of the Republic of Belarus
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.
\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.
Received: 21.10.1997
Citation:
V. V. Benyash-Krivets, “Decomposing one-relator products of cyclic groups into free products with amalgamation”, Sb. Math., 189:8 (1998), 1125–1137
Linking options:
https://www.mathnet.ru/eng/sm332https://doi.org/10.1070/sm1998v189n08ABEH000332 https://www.mathnet.ru/eng/sm/v189/i8/p13
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