Reconstruction of the extended gauge structure from Z' observables at future colliders.

The discovery of a new neutral gauge boson Z\ensuremath{'} with a mass in the TeV region would allow for the determination of gauge couplings of the Z\ensuremath{'} to ordinary quarks and leptons in a model-independent way. We show that these couplings in turn would allow us to determine the nature of the extended gauge structure. As a prime example we study the ${\mathrm{E}}_{6}$ group. In this case two discrete constraints on experimentally determined couplings have to be satisfied. If so, the couplings would then uniquely determine the two parameters tan \ensuremath{\beta} and \ensuremath{\delta} which fully specify the nature of the Z\ensuremath{'} within ${\mathrm{E}}_{6}$. If the Z\ensuremath{'} is part of the ${\mathrm{E}}_{6}$ gauge structure, then the ${\mathrm{M}}_{\mathrm{Z}\ensuremath{'}}$=1 TeV tan \ensuremath{\beta} and \ensuremath{\delta} could be determined to around 10% at the future colliders. The NLC provides a unique determination of the two constraints as well as of tan \ensuremath{\beta} and \ensuremath{\delta}, though with slightly larger error bars than at the CERN LHC. On the other hand, since the LHC primarily determines three out of four normalized couplings, it provides weaker constraints for the underlying gauge structure.