algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation)...

subgroup of the group other than the entire group Generating set of a ring: A subset S of a ring A generates A if the only subring of A containing S is A Generating...

of group theory, a strong generating set of a permutation group is a generating set that clearly exhibits the permutation structure as described by a...

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination...

} A subset S of a group G is called a generating set if every element of G can be represented by a word in S. When S is not a generating set for G...

. In this case, we say that the set { x 1 , … , x s } {\displaystyle \{x_{1},\dots ,x_{s}\}} is a generating set of G {\displaystyle G} or that x 1 ...

group cannot be free, since the elements of a free generating set of a free group have infinite order. In algebraic topology, the fundamental group of...

constructing expander graphs. Let G {\displaystyle G} be a group and S {\displaystyle S} be a generating set of G {\displaystyle G} . The Cayley graph Γ = Γ ( G...

Generator matrix, a matrix used in coding theory Generator (category theory) of a category, in category mathematics Generating set of a group, group generators...

Free abelian group Free group Free product Generating set of a group Group cohomology Group extension Presentation of a group Product of group subsets Schur...