We compute the \(E_2\) page of the Adams spectral sequence converging to the connective KO-theory of the second mod 2 Eilenberg–MacLane space, \(ko_*(K({\mathbb Z}_2,2))\) , where \({\mathbb Z}_2\) is the cyclic group of order 2. This required a careful analysis of the structure of \(H^*(K({\mathbb Z}_2,2);{\mathbb Z}_2)\) as a module over the subalgebra of the Steenrod algebra generated by \(\operatorname {Sq}^1\) and \(\operatorname {Sq}^2\) . Complete analysis of the spectral sequence is performed in [8].
