Abstract
Let [Formula: see text] be the split metacyclic group, where [Formula: see text] is a unit modulo [Formula: see text]. We derive an upper bound for the diameter of [Formula: see text] using an arithmetic parameter called the weight, which depends on [Formula: see text], [Formula: see text], and the order of [Formula: see text]. As an application, we show how this would determine a bound on the diameter of an arbitrary metacyclic group.
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