infinite subgroup

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• Subgroup series — In mathematics, a subgroup series is a chain of subgroups: Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important… …   Wikipedia

• Subgroup — This article is about the mathematical concept For the galaxy related concept, see Galaxy subgroup. Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum …   Wikipedia

• Subgroup growth — Im mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. [citebook|title=Subgroup Growth|author=Alexander Lubotzky, Dan Segal|year=2003|publisher=Birkhäuser|id=ISBN… …   Wikipedia

• Torsion subgroup — In the theory of abelian groups, the torsion subgroup AT of an abelian group A is the subgroup of A consisting of all elements that have finite order. An abelian group A is called a torsion (or periodic) group if every element of A has finite… …   Wikipedia

• Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… …   Wikipedia

• Pure subgroup — In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas.DefinitionA subgroup S of a… …   Wikipedia

• Characteristic subgroup — In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.[1][2] Because conjugation is an automorphism, every… …   Wikipedia

• Normal subgroup — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Fitting subgroup — In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G , named after Hans Fitting, is the unique largest normal nilpotent subgroup of G . Intuitively, it represents the smallest… …   Wikipedia

• Maximal subgroup — Lattice of subgroups of the symmetric group S4 M. s. are A4, three Dih4 and four S3 (Compare: Subgroups of S …   Wikipedia

• Ascendant subgroup — In mathematics, in the field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group, such that every term in the series is a normal subgroup of its… …   Wikipedia