Suppose is a finite group and a prime, such that none of the prime divisors of are congruent to modulo . We prove an equivariant analogue of Adams’ result that . We use this to show that the –connected cover of , when completed at , splits up to homotopy as a product, where one of the factors of the splitting contains the image of the classical equivariant –homomorphism on equivariant homotopy groups.
"The equivariant $J$–homomorphism for finite groups at certain primes." Algebr. Geom. Topol. 9 (4) 1885 - 1949, 2009. https://doi.org/10.2140/agt.2009.9.1885