Homework Statement
Let H, K be subgroups of a finite group G. Consider the map, f : H \times K \rightarrow HK : (h,k)\rightarrow hk. Describe f^{-1}(hk) in terms of h, k and the elements of H\cap K.
Homework Equations
HK = \{hk : h \in H, k \in K \}
f^{-1}(hk)=\{ (h',k') : f(h',k')=hk...