Abstract
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 N G (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 N G (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.
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