Kernels of the restriction and inflation maps in group cohomology

Abstract

We consider the kernel of the restriction map in group cohomology with coefficients in a field. Johnson has shown that when the subgroup is of index 2, the kernel is principal. We show that the natural generalization of this principal ideal need not be the entire kernel when the index is an odd prime or composite. We also show that the kernel of the inflation map from a central subgroup of order 2 can be larger than what might naturally be expected. © 1992.