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Diameter of a direct power of a finite group (1506.02695v2)
Published 8 Jun 2015 in math.GR
Abstract: We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gn with respect to any generating set is at most n(|G|-rank(G)); and the second one states that there exists a generating set A, of minimum size, for Gn such that the diameter of Gn with respect to A is at most n(|G|-rank(G)). We will establish evidence for each of the above mentioned conjectures.
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