A lower-bound for the number of conjugacy classes of A_n

2023/10/18 by Xandru Mifsud, Mifsud, Xandru
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Finite Group Theory Research #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2310.12047

Abstract

We establish a sharp lower-bound for the number of conjugacy classes k(A_n) in the alternating group A_n, for n ≥ 3. Namely, we show that k(A_n) ≥ (k(A₇))/(log₂|A₇|) ⋅ log₂|A_n| with equality if, and only if, n = 7. The observations leading towards this result were obtained through a genetic algorithm developed to search for groups having certain properties.

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