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- P. E. Holmes
- 2007

We present an algorithm to reduce the constructive membership problem for a black-box group G to three instances of the same problem for involution centralisers in G. If G is a simple group of Lie type in odd characteristic, then this reduction can be performed in (Monte Carlo) polynomial time.

We show that the product replacement algorithm can be used be produce random elements of the Monster group. These random elements are shown to have the same distribution of element orders as uniformly distributed random elements after a small number of steps.

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