## Cyclic extensions of parafree groups

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- by Peng Choon Wong
- Trans. Amer. Math. Soc.
**258**(1980), 441-456 - DOI: https://doi.org/10.1090/S0002-9947-1980-0558183-0
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## Abstract:

Let $1 \to F \to G \to T \to 1$ be a short exact sequence where*F*is parafree and

*T*is infinite cyclic. We examine some properties of

*G*when $F/F’$ is a free

*ZT*-module. Here $F’$ is the commutator subgroup of

*F*and

*ZT*is the integral group ring of

*T*. In particular, we show

*G*is parafree and ${\gamma _n}F/{\gamma _{n + 1}}F$ is a free

*ZT*-module for every $n \geqslant 1$ (where ${\gamma _n}F$ is the

*n*th term of the lower central series of

*F*).

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## Bibliographic Information

- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**258**(1980), 441-456 - MSC: Primary 20F12
- DOI: https://doi.org/10.1090/S0002-9947-1980-0558183-0
- MathSciNet review: 558183