Residual linearity for certain nilpotent groups
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Addendum: Proc. Amer. Math. Soc. 77 (1979), 19-22.
Abstract:
In this note we consider relations between residual finiteness and residual linearity for a nilpotent group G. We show, amongst other things, that if the center and the commutator subgroup of G are finitely generated and G is residually linear, then G is residually finite. Indeed the property which we use on linear groups is that linear groups satisfy the minimal condition on centralizers.References
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62. MR 87652, DOI 10.1112/plms/s3-7.1.29
- Robert B. Warfield Jr., Nilpotent groups, Lecture Notes in Mathematics, Vol. 513, Springer-Verlag, Berlin-New York, 1976. MR 0409661
- B. A. F. Wehrfritz, A note on residual properties of nilpotent groups, J. London Math. Soc. (2) 5 (1972), 1–7. MR 302767, DOI 10.1112/jlms/s2-5.1.1 —, Infinite linear groups, Springer-Verlag, Berlin, 1973.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 27-31
- MSC: Primary 20E15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0460465-4
- MathSciNet review: 0460465