We give a new construction of
all Steenrood cyclic reduced powers 𝒫i and of Pontrjagin-Thomas p-th powers ℬp
for each prime p. The cohomology operations are indued by operations,
analogous to the p-fold cup-i products, defined in the deRham complex of
Cartan-Miller. These operations form a basis of all the cohomology operations
derived from cyclic groups. This extends the construction of the Steenrod squares
based on the analogue of the cup-i product in the deRham complex. From
the construction of these new operations in the deRham complex it follows
that the commutative cochain problem does not have a solution over the
integers.
