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- Imperfect_group abstract "In mathematics, in the area of algebra known as group theory, an imperfect group is a group with no nontrivial perfect quotients. Some of their basic properties were established in (Berrick & Robinson 1993). The study of imperfect groups apparently began in (Robinson 1972).The class of imperfect groups is closed under extension and quotient groups, but not under subgroups. If G is a group, N, M are normal subgroups with G/N and G/M imperfect, then G/(N∩M) is imperfect, showing that the class of imperfect groups is a formation. The (restricted or unrestricted) direct product of imperfect groups is imperfect.Every solvable group is imperfect. Finite symmetric groups are also imperfect. The general linear groups PGL(2,q) are imperfect for q an odd prime power. For any group H, the wreath product H wr Sym2 of H with the symmetric group on two points is imperfect. In particular, every group can be embedded as a two-step subnormal subgroup of an imperfect group of roughly the same cardinality (2|H|2).".
- Imperfect_group wikiPageID "4939209".
- Imperfect_group wikiPageRevisionID "468916285".
- Imperfect_group hasPhotoCollection Imperfect_group.
- Imperfect_group subject Category:Group_theory.
- Imperfect_group subject Category:Properties_of_groups.
- Imperfect_group type Abstraction100002137.
- Imperfect_group type Possession100032613.
- Imperfect_group type PropertiesOfGroups.
- Imperfect_group type Property113244109.
- Imperfect_group type Relation100031921.
- Imperfect_group comment "In mathematics, in the area of algebra known as group theory, an imperfect group is a group with no nontrivial perfect quotients. Some of their basic properties were established in (Berrick & Robinson 1993). The study of imperfect groups apparently began in (Robinson 1972).The class of imperfect groups is closed under extension and quotient groups, but not under subgroups.".
- Imperfect_group label "Imperfect group".
- Imperfect_group sameAs m.0cw43m.
- Imperfect_group sameAs Q6006292.
- Imperfect_group sameAs Q6006292.
- Imperfect_group sameAs Imperfect_group.
- Imperfect_group wasDerivedFrom Imperfect_group?oldid=468916285.
- Imperfect_group isPrimaryTopicOf Imperfect_group.