conjugate subgroups

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• Conjugate-permutable subgroup — In mathematics, in the field of group theory, a conjugate permutable subgroup is a subgroup that commutes with all its conjugate subgroups. The term was introduced by Tuval Foguel in 1996 and arose in the context of the proof that for finite… …   Wikipedia

• Conjugate closure — In group theory, the conjugate closure of a subset S of a group G is the subgroup of G generated by SG, i.e. the closure of SG under the group operation, where SG is the conjugates of the elements of S: SG = {g−1sg | g ∈ G and s ∈ S} The… …   Wikipedia

• Conjugacy class — In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non abelian groups reveals many important… …   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

• Burnside ring — In mathematics, the Burnside ring of a finite group is an algebraic construction that encodes the different ways the group can act on finite sets. The ideas were introduced by William Burnside at the end of the nineteenth Century, but the… …   Wikipedia

• Carter subgroup — In mathematics, especially in the field of group theory, a Carter subgroup of a finite group G is a subgroup H that is a nilpotent group, and self normalizing. These subgroups were introduced by Roger Carter, and marked the beginning of the post… …   Wikipedia

• Point groups in three dimensions — In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries… …   Wikipedia

• Symmetry group — Not to be confused with Symmetric group. This article is about the abstract algebraic structures. For other meanings, see Symmetry group (disambiguation). A tetrahedron can be placed in 12 distinct positions by rotation alone. These are… …   Wikipedia

• Dihedral group of order 6 — The smallest non abelian group has 6 elements. It is a dihedral group with notation D3 (or D6, both are used) and the symmetric group of degree 3, with notation S3. This page illustrates many group concepts using this group as example. Contents 1 …   Wikipedia

• Automorphisms of the symmetric and alternating groups — In group theory, a branch of mathematics, the automorphisms and outer automorphisms of the symmetric groups and alternating groups are both standard examples of these automorphisms, and objects of study in their own right, particularly the… …   Wikipedia

• Triangular matrix — In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix where the entries either below or above the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve… …   Wikipedia