Reduced fiber bundles and symmetries of gauge field theories rigid reductions and the einstein-cartan theory

The process of the reduction of a principal fibre bundle P(M, G) to a reduced subbundle Q(M, H) is analysed in view of applications to the description of symmetries of gauge theories. The main idea is to relate symmetries of the nonuniqueness of the reduction by gauging the different ways in which for each fiber the unbroken group H is imbedded into the large group G. Gauge theories encompassing gravitation are especially taken into account.