One relator groups having a finitely presented normal subgroup

Authors:
A. Karrass and D. Solitar

Journal:
Proc. Amer. Math. Soc. **69** (1978), 219-222

MSC:
Primary 20F05

MathSciNet review:
0466323

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Abstract: A classification is given for one-relator groups having a finitely presented normal subgroup of infinite index.

**[1]**Gilbert Baumslag,*Finitely generated cyclic extensions of free groups are residually finite*, Bull. Austral. Math. Soc.**5**(1971), 87–94. MR**0311776****[2]**Robert Bieri,*Homological dimension of discrete groups*, Mathematics Department, Queen Mary College, London, 1976. Queen Mary College Mathematics Notes. MR**0466344****[3]**Ian M. Chiswell,*Euler characteristics of groups*, Math. Z.**147**(1976), no. 1, 1–11. MR**0396785****[4]**J. Fischer, A. Karrass, and D. Solitar,*On one-relator groups having elements of finite order*, Proc. Amer. Math. Soc.**33**(1972), 297–301. MR**0311780**, 10.1090/S0002-9939-1972-0311780-0**[5]**A. Karrass, A. Pietrowski, and D. Solitar,*An improved subgroup theorem for HNN groups with some applications*, Canad. J. Math.**26**(1974), 214–224. MR**0432766****[6]**A. Karrass and D. Solitar,*Subgroups of 𝐻𝑁𝑁 groups and groups with one defining relation*, Canad. J. Math.**23**(1971), 627–643. MR**0301102****[7]**A. Karrass and D. Solitar,*The subgroups of a free product of two groups with an amalgamated subgroup*, Trans. Amer. Math. Soc.**150**(1970), 227–255. MR**0260879**, 10.1090/S0002-9947-1970-0260879-9**[8]**John Stallings,*Groups of cohomological dimension one*, Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVIII, New York, 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 124–128. MR**0255689**

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0466323-3

Keywords:
One-relator groups

Article copyright:
© Copyright 1978
American Mathematical Society