[GAP Forum] G-invariant bimultiplicative maps

[Dan Lanke]

Dear GAP Forum,

Let G be a finite group and let K, H be a pair of normal subgroups of G.
Let C* denote the multiplicative group of nonzero complex numbers.

Is there a way to determine all (or atleast some) G-invariant bimultiplicative maps
f: K x H -> C* ?

f is a G-invariant bimultiplicative map means:

f(kk', h) = f(k, h) f(k', h), for all k,k' \in K, h \in H,

f(k, hh') = f(k, h) f(k, h'), for all k \in K, h,h' \in H,

and

f(gkg^{-1}, ghg^{-1}) = f(k, h), for all g \in G, k \in K, h \in H.

Many thanks,
Dan