(2) If G is a finite group then the sum in the exponential is a finite sum running over all subgroups of G, and continuous homomorphisms from G to Sn are simply homomorphisms from G to Sn. The result in this case is due to Wohlfahrt (1977). The special case when G is a finite cyclic group is due to Chowla, Herstein, and Scott (1952), and takes the form
If G is a finite group, the sum in the exponential is a finite sum over all subgroups of G, and continuous homomorphisms from G to Sn are simply homomorphisms from G to Sn. This result was established by Wohlfahrt in 1977. The special case when G is a finite cyclic group is due to Chowla, Herstein, and Scott (1952), and takes the form