Cyclic extensions of parafree groups
Let 1 —> F —> G —> T —> 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 Zr-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...
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| Format: | Article |
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American Mathematical Society
1980
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| Online Access: | http://eprints.um.edu.my/13173/ https://www.ams.org/journals/tran/1980-258-02/S0002-9947-1980-0558183-0/S0002-9947-1980-0558183-0.pdf |
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| Summary: | Let 1 —> F —> G —> T —> 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 Zr-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 y„F/y„+
XF is a free Z7"-module for every n > 1 (where ynF is the nth term of the lower central series of F). |
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