  The question of the role of the center of the gauge group in the phenomenon
of confinement in Yang-Mills theory is addressed. The investigation is
performed from the most general perspective of considering all possible choices
for the gauge symmetry group. In this context, an interesting role is played by
G(2) Yang-Mills theory: the simplest pure gauge theory with a trivial center
and without 't Hooft flux vortices. Numerical simulations show the presence of
a first order finite temperature deconfinement phase transition in G(2)
Yang-Mills theory in (3+1) dimensions. Interestingly, the G(2) gauge symmetry
can be broken to an SU(3) subgroup by the Higgs mechanism. We investigate the
relation between the deconfinement phase transition in G(2) and SU(3)
Yang-Mills theories by numerical simulations in the G(2) gauge-Higgs system.
