  The best known method to give a lower bound for the Noether number of a given
finite group is to use the fact that it is greater than or equal to the Noether
number of any of the subgroups or factor groups. The results of the present
paper show in particular that these inequalities are strict for proper
subgroups or factor groups. This is established by studying the algebra of
coinvariants of a representation induced from a representation of a subgroup.
