Lower defect groups in symmetric groups, J. Algebra 104 (1986), 37-56.

The final result Proposition (3.19) is not quite correct as stated. The problem is that the definition of
e(\lambda) needs to be modified. For details see Theorem 4.5 in the paper

C. Bessenrodt, J.B. Olsson: Spin representations and powers of 2 ,
    Algebras and Representation Theory  3 (2000), 289-300, preprint.