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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Cyclic extensions of parafree groups


Author: Peng Choon Wong
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
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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 nth term of the lower central series of F).


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DOI: https://doi.org/10.1090/S0002-9947-1980-0558183-0
Keywords: Free group, parafree groups, free nilpotent groups, free module, integral group ring
Article copyright: © Copyright 1980 American Mathematical Society