21st Annual Symposium on Foundations of Computer Science (sfcs 1980) (1980)
Oct. 13, 1980 to Oct. 15, 1980
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/SFCS.1980.34
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 testing are decidable in polynomial time. In addition, we demonstrate that the normal closure of a subgroup can be computed in polynomial time, and that this proceaure 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.
J. Hopcroft, M. Furst and E. Luks, "Polynomial-time algorithms for permutation groups," 21st Annual Symposium on Foundations of Computer Science (sfcs 1980)(FOCS), vol. 00, no. , pp. 36-41, 1980.