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Testing commutativity of a group and the power of randomization

Part of: Special aspects of infinite or finite groups Theory of computing

Published online by Cambridge University Press:  01 April 2012

Igor Pak
Igor Pak*
Affiliation:
Department of Mathematics, University of California, Los Angeles, 530 Portola Plazza 6363 Math Sciences Building Los Angeles, CA 90095-1555, USA (email: pak@math.ucla.edu)

Abstract

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Let G be a group generated by k elements, G=〈g1,…,gk〉, with group operations (multiplication, inversion and comparison with identity) performed by a black box. We prove that one can test whether the group G is abelian at a cost of O(k) group operations. On the other hand, we show that a deterministic approach requires Ω(k2) group operations.

MSC classification

Secondary: 20F69: Asymptotic properties of groups 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 38 - 43
Copyright
Copyright © London Mathematical Society 2012

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