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The algebraic transfer is an important tool to study the cohomology of the Steenrod algebra. In this study, we will construct a version of the algebraic transfer in E 2 -term of May spectral sequence and use this version to study the image of the algebraic transfer. By this method, we obtain the description of the image of ϕ s in some degrees.

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 E 2 version of the algebraic transfer are compatible. We also prove that the two Sq 0 -families n i ∈ Ext 5,36·2 i A (Z/2, Z/2), i ≥ 0, and k i ∈ Ext 7,36·2 i A (Z/2, Z/2), i ≥ 1, are in the image of the algebraic transfer.

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