Back Charakteristische Untergruppe German زیرگروه مشخصه Persian Sous-groupe caractéristique French Karakterisztikus részcsoport Hungarian Subgrup karakteristik ID Sottogruppo caratteristico Italian 特性部分群 Japanese 특성 부분군 Korean Karakteristieke ondergroep Dutch Podgrupa charakterystyczna Polish
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.[1][2] 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.
- ^ Dummit, David S.; Foote, Richard M. (2004). Abstract Algebra (3rd ed.). John Wiley & Sons. ISBN 0-471-43334-9.
- ^ Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. Springer. ISBN 0-387-95385-X.