Xue, X (reprint author), E China Normal Univ, Dept Phys, Inst Theoret Phys, Shanghai 200241, Peoples R China.
We investigate here various kinds of semi-product subgroups of Poincare group in the scheme of Cohen-Glashow's very special relativity along the deformation approach by Gibbons- Gomis-Pope. For each proper Poincare subgroup which is a semi-product of proper lorentz group with the spacetime translation group T(4), we investigate all possible deformations and obtain all the possible natural representations inherited from the 5 - d representation of Poincare group. We find from the obtained natural representation that rotation operation may have additional accompanied scale transformation when the original Lorentz subgroup is deformed and the boost operation gets the additional accompanied scale transformation in all the deformation cases. The additional accompanied scale transformation has a strong constrain on the possible invariant metric function of the corresponding geometry and the field theories in the spacetime with the corresponding geometry.