Subgroup properties

Characteristic subgroup

In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by every automorphism of the parent group. Because every conjugation map is an inner automorphism, every characteristic subgroup is normal; though the converse is not guaranteed. Examples of characteristic subgroups include the commutator subgroup and the center of a group. (Wikipedia).

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From playlist Abstract algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Unit 1: Descriptive Statistics

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From playlist Galois theory

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From playlist Mathematics

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From playlist PROBABILISTIC METHODS IN NEGATIVE CURVATURE - 2023

Related pages

Verbal subgroup | Klein four-group | Invariant (mathematics) | Automorphism | Free group | Topological group | Index of a subgroup | Group (mathematics) | Torsion subgroup | Symmetric group | Group isomorphism | Quotient group | Identity component | Finite group | Direct product of groups | Transitive relation | Dihedral group | Mathematics | Characteristically simple group | Cyclic group | Group theory | Normal subgroup | Subgroup | Abstract algebra | Commutator subgroup | Conjugacy class | Endomorphism | Abelian group | Outer automorphism group | Inner automorphism | Quaternion group