Sylow subgroups are fundamental in the design of asymptotically efficient g
roup-theoretic algorithms, just as they have been in the study of the struc
ture of finite groups. We present efficient parallel (NC) algorithms for fi
nding and conjugating Sylow subgroups of permutation groups, as well as for
related problems. Polynomial-time solutions to these problems were obtaine
d more than a dozen years ago, exploiting a well-developed polynomial-time
library. We replace some of those highly sequential procedures with ones th
at work through a polylog-length normal series that is a by-product of NC m
embership-testing. As in previous investigations, we reduce to the base cas
e of simple groups, and handle this by a case-by-case analysis that depends
heavily upon the classification of finite simple groups. (C) 1999 Academic
Press.