Computing Intersections and Normalizers in Soluble Groups
Journal of Symbolic Computation
Let H and K be arbitrary subgroups of a finite soluble group G. The purpose of this paper is todescribe algorithms for constructing H∩K and NG(H). The first author has previously described algorithms for constructing H∩K when the indices |G:H| and |G:K| are coprime, and for constructing NG(H) when |G:H| and |H| are coprime (i.e. when H is a Hall subgroup of G). The intersection and normalizer algorithms described in the present paper are constructed from generalizations of these algorithms and from an orbit-stabilizer algorithm.