FACTOR EQUIVALENCE OF RINGS OF INTEGERS AND CHINBURG INVARIANT IN THEDEFECT CLASS GROUP

Let GAMMA be a finite group. We introduce the factorizability defect, fd, defined on exact sequences in mod (ZGAMMA). Let C be the subcatego ry of mod(ZGAMMA) of modules with finite projective dimension away fro m a finite set S of integer primes. We examine the defect class group Cl(C(fd)) (the subgroup of locally trivial elements in the defect Grot hendieck group, K0(C(fd)) and show that it is isomorphic to the direct sum class group of C. Let N/K be a Galois extension of algebraic numb er fields with group GAMMA which is tamely ramified outside S. We show that [O(N)]-[O(K)GAMMA] lies in Cl(C(fd)) and equals the image of OME GA(N/K,2), Chinburg's second invariant. We also show that if M and M' lie in C and [M]-[M'] is-an-element-of Cl(C(fd)) then M is factor equi valent to M' in a very strong sense. In particular O(N) is factor equi valent in this way to a free ZGAMMA-module.