Permutation Summands Over Z Original Research Article

A permutation lattice for a finite group G is a free Z-module with a finite basis which is permuted by G; direct summands of these, as ZG-module, are the lattices of the title. Numerical genus invariants are constructed for these lattices by globalizing the "species" of Benson and Parker. These are used to study the Grothendieck ring of the category of permutation summands. The Galois module structure of cyclotomic integers plays a role.