Let G be a finite group, and let r₃(G) represent the size of the largest subset of G without non-trivial three-term progressions. In a recent breakthrough, Croot, Lev and Pach proved that r₃(C4n) ≤ (3.611)ⁿ, where C_m denotes the cyclic group of order m. For finite abelian groups G≅∏i=1nCmi, where m₁,…,m_n denote positive integers such that m₁ |…|m_n, this also yields a bound of the form r3(G)⩽(0.903)rk4(G)|G|, with rk4(G) representing the number of indices i ∈ {1,…, n} with 4 |m_i. In particular, r₃(C8n) ≤ (7.222)ⁿ. In this paper, we provide an exponential improvement for this bound, namely r₃(C8n) ≤ (7.0899)ⁿ.