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We study the Mahowald operator $M = \langle g_2,h_0^3, - \rangle$ in thecohomology of the Steenrod algebra. We show that the operator interacts wellwith the cohomology of $A(2)$, in both the classical and $\mathbb{C}$-motiviccontexts. This generalizes previous work of Margolis, Priddy, and Tangora.

The Mahowald operator in the cohomology of the Steenrod algebra