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In the context of η- μ generalized fading scenarios, this paper provides a general closed-form expression for the average symbol error probability (SEP) of arbitrary M-ary quadrature amplitude modulation (QAM) constellations in maximal-ratio combining (MRC) schemes over non-identical correlated channels. For such a scenario, the moment-generating function (MGF) of the signal-to-noise ratio (SNR) at the combiner output is obtained by rearranging the Gaussian components used to model the correlation between the diversity branches. The average SEP is then derived in terms of Lauricella multivariate hypergeometric functions, which can be implemented in most popular numerical softwares, such as Mathematica. The proposed analytical expressions are validated through Monte Carlo simulations, and insightful discussions are provided from the numerical results.