Evaluating logarithms in GF(2n)
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Computing modular and projective character degrees of soluble groups
Journal of Symbolic Computation
Computing intersections and normalizersin soluble groups
Journal of Symbolic Computation
Computing sylow subgroups of permutation groups using homomorphic images of centralizers
Journal of Symbolic Computation - Special issue on computational group theory: part 2
Experimental comparison of algorithms for Sylow subgroups
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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This paper describes algorithms for constructing a Hall @p-subgroup H of a finite soluble group G and the normaliser N"G(H). If G has composition length n, then H and N"G(H) can be constructed using O(n^4 log |G|) and O(n^5 log |G|) group multiplications, respectively. These algorithms may be used to construct other important subgroups such as Carter subgroups, system normalisers and relative system normalisers. Computer implementations of these algorithms can compute a Sylow 3-subgroup of a group with n = 84, and its normaliser in 47 seconds and 30 seconds, respectively. Constructing normalisers of arbitrary subgroups of a finite soluble group can be complicated. This is shown by an example where constructing a normaliser is equivalent to constructing a discrete logarithm in a finite field. However, there are no known polynomial algorithms for constructing discrete logarithms.