Bulletin of the
Korean Mathematical Society BKMS

The algebraic structure of the natural integral cohomology operations is explored by means of examples. We decompose the generators of the groups $H^m(\mathbb{Z},n)$ with $2 \leq n \leq 7$ and $2 \leq m \leq 13$ into the operations of cup products, cross-cap products and compositions. Examination of these decompositions and comparison with other possible generators demonstrates the existence of relations between integral operations that have withheld formulation. The calculated groups and generators are collected in a table for practical reference.

Keywords: integral cohomology operation, relations

MSC numbers: 55S05