We use work of Curtis and Wellington on A-annihilated classes in H_*QS⁰ together with Priddy's computations on the action of the Dyer-Lashof algebra on
H_*(Z x BO) to provide new examples of A-annihilated classes in H_*BO as well H_*BO(2^r-1). We then consider the Becker-Gottlieb transfer associated to O(1)^xn → O(n) and speculate on the possible applications of our computations to obtain new examples of A-annihilated classes in H_*BO(1)ⁿ. Our results, all at the prime p=2, provide new numerical conditions which seem to show up for the first time in this context.

This work is partially supported by a grant from the Iranian National Science Foundation (INSF) Grant No. 98023105.