In this paper, some results on the superfluous subgroups of a finitely-generated infinite soluble group are obtained, which are the generalizations of the corresponding results of a finite group.
Group-graded rings of half-simple modules with finitely generated modules;
finitely additive probabiltity measure
finitely generatable vector space
there are finitely many solutions to this problem.
The emergence of over-education not only wastes finitely educational resources, but also brings negative impacts on sustained, rapid economic growth.
We also obtain that for a finitely generated transcendental semigroup, there is a best generating set.