Efficient isomorphism testing for a class of group extensions

Leibniz International Proceedings in Informatics, LIPIcs

Volumn 3, Issue , 2009, Pages 625-636

  Le Gall, François ^a  

^a JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

Black box groups; Group isomorphism; Polynomial time algorithms

Indexed keywords

ABELIAN GROUP; BLACK-BOX GROUPS; GROUP EXTENSION; GROUP ISOMORPHISM; ISOMORPHISM PROBLEMS; ISOMORPHISM TESTING; NON-ABELIAN GROUPS; POLYNOMIAL-TIME ALGORITHMS;

ALGORITHMS; COMPUTER SCIENCE;

SET THEORY;

EID: 79955722468     PISSN: 18688969     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. V. Arvind and J. Torán. Solvable group isomorphism. In Proceedings of the 19th IEEE Conference on Computational Complexity, pages 91-103, 2004.
2. L. Babai. Trading group theory for randomness. In Proceedings of the 17th annual ACM symposium on Theory of computing, pages 421-429, 1985.
3. L. Babai. Local expansion of vertex-transitive graphs and random generation in finite groups. In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 164-174, 1991.
4. L. Babai and E. Szemerédi. On the complexity of matrix group problems I. In Proceedings of the 25th Annual Symposium on Foundations of Computer Science, pages 229-240, 1984.
5. J. Buchmann and A. Schmidt. Computing the structure of a finite abelian group. Mathematics of Computation, 74(252):2017-2026, 2005.
6. T. J. Chou and G. E. Collins. Algorithms for the solution of systems of linear diophantine equations. SIAM Journal on Computing, 11(4):687-708, 1982.
7. M. H. Garzon and Y. Zalcstein. On isomorphism testing of a class of 2-nilpotent groups. Journal of Computer and System Sciences, 42(2):237-248, 1991.
8. G. H. Hardy and E. M. Wright. An introduction to the theory of numbers. Oxford Science Publications, 1979.
9. D. F. Holt, B. Eick, and E. A. O'Brien. Handbook of computational group theory. Chapman & Hall/CRC, 2005.
10. R. Kannan and A. Bachem. Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix. SIAM Journal on Computing, 8(4):499-507, 1979.
11. T. Kavitha. Linear time algorithms for abelian group isomorphism and related problems. Journal of Computer and System Sciences, 73(6):986-996, 2007.
12. J. Köbler, J. Torán, and U. Schöning. The graph isomorphism problem: its structural complexity. Birkhäuser, 1993.
13. R. J. Lipton, L. Snyder, and Y. Zalcstein. The complexity of word and isomorphism problems for finite groups. Technical report, John Hopkins, 1976.
14. logn isomorphism technique. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing, pages 51-58, 1978.
15. E. A. O'Brien. Isomorphism testing for p-groups. Journal of Symbolic Computation, 17:133-147, 1994.
16. J. Pomfret. Similarity of matrices over finite rings. Proceedings of the American Mathematical Society, 37(2):421-422, 1973.
17. A. Ranum. The group of classes of congruent matrices with application to the group of isomorphisms. Transactions of the American Mathematical Society, 8(1):71-91, 1907.
18. S. Shanks. Class number, a theory of factorization and generata. Proceedings of Symposia in Pure Mathematics, 20(419-440), 1969.
19. V. Shoup. A computational introduction to number theory and algebra. Cambridge University Press, 2005.
20. M. Smith. Computing automorphisms of finite soluble groups. PhD thesis, Australian National University, 1994.
21. A. K. Steel. Algorithm for the computation of canonical forms of matrices over fields. Journal of Symbolic Computation, 24(3/4):409-432, 1997.
22. N. Vikas. An O(n) algorithm for abelian p-group isomorphism and an O(nlog n) algorithm for abelian group isomorphism. Journal of Computer and System Sciences, 53(1):1-9, 1996.