Transgressive elements in Hopf algebra spectral sequence

Let $$E^r$$ be a commutative Hopf algebra homology spectral sequence over $$\mathbb{Z}/p$$, i.e. such that every sheet is a commutative Hopf algebra.

I am struggling with proving (probably simple) fact - that every transgressive element in such a spectral sequence is primitive.

• How do the differentials interact with the Hopf algebra structure? – Denis Nardin Mar 5 at 21:44
• They are morphisms of Hopf algebras, and are derivations w.r.t. multiplication and the tensor product, as far as I understand. – Igor Sikora Mar 6 at 15:02
• How can they be both morphisms of Hopf algebras and (co?)derivations? – Denis Nardin Mar 6 at 15:32
• Sorry, you are right - a multiplication and comultiplication should be morphisms of spectral sequences. Hopefully it makes sense now – Igor Sikora Mar 6 at 15:44