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Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Lower bounds for the R\u00e9nyi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in prime cyclic groups building on Lev [ Duke Math. J., 107 (2001), pp. 239--263] and notions of stochastic ordering. 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