Groups with super-exponential subgroup growth

Groups with super-exponential subgroup growth Groups with super-exponential subgroup growth

L. Pyber, A. Shalev:

Groups with super-exponential subgroup growth

We show that, if the subgroup growth of a finitely generated group G is super-exponential, then every finite group occurs as a quotient of a finite index subgroup of G. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.