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Polynomial-time algorithms for permutation groups

Author: Merrick Lee Furst; John E Hopcroft; Eugene Luks
Publisher: Ithaca, N.Y. : Dept. of Computer Science, Cornell University, 1980.
Series: Technical report (Cornell University. Department of Computer Science), TR 80-442.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
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,  Read more...
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Details

Document Type: Book
All Authors / Contributors: Merrick Lee Furst; John E Hopcroft; Eugene Luks
OCLC Number: 63578955
Notes: Typescript.
Description: 15 pages ; 28 cm.
Series Title: Technical report (Cornell University. Department of Computer Science), TR 80-442.
Responsibility: Merrick Furst, John Hopcroft, Eugene Luks.

Abstract:

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 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.

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