Universal deformation rings and fusion

We study in this paper the extent to which one can detect fusion in certain finite groups Γ   from information about the universal deformation rings R(Γ,V)R(Γ,V) of absolutely irreducible FpΓFpΓ-modules V. The Γ we consider are extensions of either abelian or dihedral groups G of order prime to p by an elementary abelian p-group of rank 2.