The equivariantJ–homomorphism for finite groups at certain primes

Abstract

Suppose G is a finite group and p a prime, such that none of the prime divisors of G are congruent to 1 modulo p. We prove an equivariant analogue of Adams’ result that J′=J′′. We use this to show that the G–connected cover of QGS0, when completed at p, splits up to homotopy as a product, where one of the factors of the splitting contains the image of the classical equivariant J–homomorphism on equivariant homotopy groups.