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We consider algorithms for computing intersections and normalizers of subgroups in finitely generated nilpotent groups. In Glasby (1988a, b) and Glasby and Slattery (1990), algorithms for computing intersections and normalizers in finite solvable groups from AG-systems (see Laue et al, 1984) are described. In Baumslag et al. (1991), algorithms to find intersections and normalizers of subgroups in polycyclic-by-finite groups were described. However, the algorithms there are not practical for computer implementation. In this article, practical algorithms to compute intersections and normalizers of subgroups in finitely generated nilpotent groups from nilpotent presentations are developed. These ideas are extended to give practical algorithms to determine membership in products of subgroups and to determine conjugacy of subgroups. A test for nilpotency is also descried for polycyclic groups. A prototype Mathematica program has been written to test the efficency of some of the algorithms described here. The results are tabulated in the last section.
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