B subgroup element

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• 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 test — In Abstract Algebra, the one step subgroup test is a theorem that states that for any group, a subset of that group is itself a group if the inverse of any element in the subset multiplied with any other element in the subset is also in the… …   Wikipedia

• subgroup — /sub groohp /, n. 1. a subordinate group; a division of a group. 2. Chem. a division of a group in the periodic table. 3. Math. a subset of a group that is closed under the group operation and in which every element has an inverse in the subset.… …   Universalium

• subgroup — sub•group [[t]ˈsʌbˌgrup[/t]] n. 1) a subordinate group 2) math. Math. a subset of a group that is closed under the group operation and in which every element has an inverse in the subset • Etymology: 1835–45 …   From formal English to slang

• 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

• Quasinormal subgroup — In mathematics, in the field of group theory, a quasinormal subgroup, or permutable subgroup, is a subgroup of a group that commutes (permutes) with every other subgroup. The term quasinormal subgroup was introduced by Oystein Ore in 1937.Two… …   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

• Frattini subgroup — Hasse diagram of the lattice of subgroups of the dihedral group Dih4 In the 3 element layer are the maximal subgroups; their intersection (the F. s.) is the central element in the 5 element layer. So Dih4 has only one non generating element… …   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 compact subgroup — In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. Maximal compact subgroups play an important role in the classification of …   Wikipedia