virtually nilpotent造句

Common uses for this would be when P is polynomial growth are precisely the finitely generated virtually nilpotent groups.
Beyond Gromov's theorem one can ask whether there exists a gap in the growth spectrum for finitely generated group just above polynomial growth, separating virtually nilpotent groups from others.
In 1981 he proved Gromov's theorem on groups of polynomial growth : a finitely generated group has polynomial growth ( a geometric property ) if and only if it is virtually nilpotent ( an algebraic property ).
Formally, this means that there would exist a function f : \ mathbb N \ to \ mathbb N such that a finitely generated group is virtually nilpotent if and only if its growth function is an O ( f ( n ) ).
The result obtained is actually a bit stronger since it establishes that there exists a " growth gap " between virtually nilpotent groups ( of polynomial growth ) and other groups; that is, there exists a ( superpolynomial ) function f such that any group with growth function bounded by a multiple of f is virtually nilpotent.
It's difficult to find virtually nilpotent in a sentence. 用virtually nilpotent造句挺难的

The result obtained is actually a bit stronger since it establishes that there exists a " growth gap " between virtually nilpotent groups ( of polynomial growth ) and other groups; that is, there exists a ( superpolynomial ) function f such that any group with growth function bounded by a multiple of f is virtually nilpotent.