On the May spectral sequence and the algebraic transfer II

We study the algebraic transfer constructed by Singer [19] using the May spectral sequence technique. We show that the two squaring operators defined by Kameko [8] and Nakamura [16] on the domain and range respectively of our E2E2 version of the algebraic transfer are compatible. We also prove that the two Sq0Sq0-families ni∈ExtA5,36⋅2i(Z/2,Z/2), i≥0i≥0, and ki∈ExtA7,36⋅2i(Z/2,Z/2), i≥1i≥1, are in the image of the algebraic transfer.