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We study double averages along orbits for measure preserving actions of$\mathbb{A}^\omega$, the direct sum of countably many copies of a finiteabelian group $\mathbb{A}$. In this article we show an $L^p$ norm-variationestimate for these averages, which in particular reproves their convergence in$L^p$ for any finite $p$ and for any choice of two $L^\infty$ functions. Theresult is motivated by recent questions on quantifying convergence of multipleergodic averages.

Quantitative norm convergence of double ergodic averages associated with two commuting group actions