The article finds an asymptotic formula for average automorphisms in additive groups, suggesting deeper group property insights.
Let [Formula: see text] be the additive group of the residue classes modulo [Formula: see text]. For positive integers [Formula: see text] and [Formula: see text], let [Formula: see text] denote the number of the automorphisms of the group [Formula: see text]. We obtain an asymptotic formula for the sum [Formula: see text], which indicates that the average value of [Formula: see text] is [Formula: see text] up to multiplying by a constant.
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Liu et al. (2025) studied this question.
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