UCLA

This dissertation is concerned with calculating the group of unramified Brauer invariants of a finite group over a field of arbitrary characteristic. We present a formula for the group of degree-two cohomological invariants of a finite group G with coefficients in Q/Z(1) over a field F of arbitrary characteristic. We then specialize this formula to the case of decomposable invariants and compute the unramified decomposable cohomological invariants with coefficients in Q/Z(1) for various finite groups G. When the order of G is prime to the characteristic of F, we obtain a formula for the degree-two unramified normalized decomposable invariants of finite abelian G and certain nonabelian groups G. We additionally compute the degree-two unramified normalized decomposable invariants with coefficients in Q/Z(1) in the case that G is cyclic of order p over a field of characteristic p.