Linear time algorithms for Abelian group isomorphism and related problems

Journal of Computer and System Sciences

Volumn 73, Issue 6, 2007, Pages 986-996

  Kavitha, T ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Abelian; Group; Isomorphism; Nilpotent; Order

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SCIENCE; PROBLEM SOLVING;

ABELIAN GROUPS; ISOMORPHISM; MULTIPLICATION TABLES;

ALGORITHMS;

EID: 34250200778     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/j.jcss.2007.03.013     Document Type: Article

References (23)

1. Apostol T.M. Introduction to Analytic Number Theory (1997), Springer-Verlag
2. V. Arvind, Jacobo Torán, Solvable group isomorphism is (almost) in NP ∩ coNP, in: IEEE Conference on Computational Complexity, 2004, pp. 91-103
3. Babai L., Cooperman G., Finkelstein L., Luks E.M., and Seress A. Fast Monte Carlo algorithms for permutation groups. J. Comput. System Sci. 50 2 (1995) 296-308
4. Mix Barrington D.A., Kadau P., Lange K.-J., and McKenzie P. On the complexity of some problems on groups input as multiplication tables. J. Comput. System Sci. 63 2 (2001) 186-200
5. Cooperman G., and Finkelstein L. Random algorithms for permutation groups. CWI Quart. 5 (1992) 107-125
6. Garzon M., and Zalcstein Y. On isomorphism testing of a class of 2-nilpotent groups. J. Comput. System Sci. 42 (1991) 237-248
7. Hall M. Theory of Groups (1959), Macmillan Co., New York
8. Hardy G.H., and Wright E.M. An Introduction to the Theory of Numbers (1981), Oxford University Press
9. Herstein I.N. Topics in Algebra (1964), Blaisdell, New York
10. Kavitha T. Efficient algorithms for Abelian group isomorphism and related problems. Proceedings of 23rd FSTTCS. Lecture Notes in Comput. Sci. vol. 2914 (2003) 277-288
11. S. Ravi Kumar, Ronitt Rubinfeld, Property testing of Abelian group operations, manuscript
12. Köbler J., Schöning U., and Torán J. The Graph Isomorphism Problem: Its Structural Complexity (1993), Birkhäuser
13. Lipton R.J., Snyder L., and Zalcstein Y. The Complexity of Word and Isomorphism Problems for Finite Groups (1976), John Hopkins
14. MacLane S., and Birkhoff G. Algebra (1964), Macmillan Co., New York
15. Mairson H.G. Some new upper bounds on the generation of prime numbers. Comm. ACM 20 (1977) 664-669
16. log n isomorphism technique. Proceedings of the Tenth Annual ACM Symposium on Theory of Computing (May 1978) 51-58
17. Miller G.L. Graph isomorphism, general remarks. J. Comput. System Sci. 18 (1979) 128-142
18. W. Narkiewicz, Number Theory, World Scientific Publishing Company
19. Igor Pak, Testing commutativity of a group and the power of randomization, preprint, 2000
20. Rotman J.J. An Introduction to the Theory of Groups (1995), Springer-Verlag
21. Rajagopalan S., and Schulman L. Verifying identities. Proceedings of the 35th Foundations of Computer Science (1994) 288-299
22. 2) algorithm for Abelian group isomorphism, Technical Report TR 80-01, North Carolina State University, January 1980
23. Vikas N. An O (n) algorithm for Abelian p-group isomorphism and an O (n log n) algorithm for Abelian group isomorphism. J. Comput. System Sci. 53 (1996) 1-9