Sentence examples for be a group generated from inspiring English sources

Let (G) be a group generated by a finite set (S).

Let G be a group generated by a finite set X, (Hle G) be a subgroup generated by a finite set Y. Recall that the distortion function (f_{H,G}(n)) is defined as the minimal number k such that every element of H represented as a word w of length ({le } n) in the alphabet X can be represented as a word of length ({le } k) in the alphabet Y [17].

We can choose a generating set (3.14). of in such a way that is the group generated by and.

It follows that it is possible to choose a generating set (3.3). of in such a way that is the group generated by and for each.

Let (G) be a finitely generated group with a system of generators (A={a_1,ldotsdots,a_m}) (throughout the paper we consider only infinite finitely generated groups and only finite systems of generators).

Let (G) be a finitely generated group with no free subsemigroup on two generators and let the quotient (G/N) be an elementary amenable group.

Let G be a finitely generated group and G▷G1▷G2▷⋯ be normal subgroups such that ⋂k="1∞Gk="{1}.

Let (G) be a finitely generated group.

Let (G) be a finitely generated group, (N) a normal subgroup, and (Z) a central subgroup.

Let (G) be a finitely generated group and (E) a finitely presented cover of (G).

In that case \((G, \cdot, S \) is said to be a finitely generated group.