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15.48 (2002)

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Let $G$ be any non-trivial finite group, and let $X$ be any generating set for $G$. Is it true that every element of $G$ can be obtained from $X$ using fewer than $2 \log_2 |G|$ multiplications? (When counting the number of multiplications on a path from the generators to a given element, at each step one can use the elements obtained at previous steps.)

Contributor: C. R. Leedham-Green

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