Abstract
Let ZF be the free integral group ring of the free group F generated by y l, y 2, ... . Let
be the fundamental (augmentation, basic) ideal of ZF, where \(\varepsilon \left( {\sum {{n_g}g} } \right) = \sum {{n_g}} \). If R is a normal subgroup of F, Let
where θ is the natural map of F onto F/R linearly extended to ZF. For each n ≥ 1, \({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{f} } ^n}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} } \) is a free ideal of ZF and can be identified as:
.
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References
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Gupta, C.K., Gupta, N.D. (1974). Power Series and Matrix Representations of Certain Relatively Free Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_28
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DOI: https://doi.org/10.1007/978-3-662-21571-5_28
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