On the exponent and the order of the groups $$\tilde J$$ (X)

On the Order of Certain Elements of $J(X)$ and the Adams Conjecture

“…We can prove Theorem 1 of Sigrist and Suter [18] by making use of Theorem 2.4 and Lemma 4.6. In the proof of [18], the fact that s-map induces a homomorphism of J" ( [2]) is not clear, since s-map does not commute with the Adams operations. Moreover the Atiyah transfer does not commute with the Adams operations.…”

“…By a quite similar method to the proof of Theorem 1, we can prove Theorem 1 of Sigrist and Suter [18]. § 2.…”

“…But we use relations between the induction homomorphisms and the Adams operations in [12] instead of the localization. We also use the cellular approximation of the Becker-Gottlieb transfer used by Sigrist and Suter in [18] instead of the usual Becker-Gottlieb transfer [8].…”