Logspace and compressed-word computations in nilpotent groups

For finitely generated nilpotent groups, we employ Mal’cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations for subgroups are solved using only logarithmic space and, simultaneously, in quasilinear time. Compressed-word versions of these problems, in which each input word is provided as a straight-line program, are solved in polynomial time.