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Testing commutativity of a group and the power of randomization
Published online by Cambridge University Press: 01 April 2012
Abstract
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.
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- Copyright © London Mathematical Society 2012
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