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A permutation group on n letters may always be represented by a small set of generators, even though its size may be exponential in n.We show that it is practical to use such a representation since many problems such as membership testing, equality testing, and inclusion testiLg are decidable in polynomial time.In additions we demonstrate that the normal closure of a subgroup can be computed in polynomial time, and that this procedure can be used to test a group for solvability. We also describe an approach to computing the intersection of two groups. The procedures and techniques have wide applicability and have recently been used to improve many graph isomorphism algorithms.Accession For NTIS Gr&I DTIC T.i U:annoli!-ed AVs.r n ,. t.

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