This HTML5 document contains 44 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n11https://global.dbpedia.org/id/
yagohttp://dbpedia.org/class/yago/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
provhttp://www.w3.org/ns/prov#
dbchttp://dbpedia.org/resource/Category:
dbphttp://dbpedia.org/property/
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Normal_subgroup
dbo:wikiPageWikiLink
dbr:Imperfect_group
Subject Item
dbr:Imperfect_(disambiguation)
dbo:wikiPageWikiLink
dbr:Imperfect_group
dbo:wikiPageDisambiguates
dbr:Imperfect_group
Subject Item
dbr:Imperfect_group
rdf:type
yago:Possession100032613 yago:Relation100031921 yago:Property113244109 yago:WikicatPropertiesOfGroups yago:Abstraction100002137
rdfs:label
Imperfect group
rdfs: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. The study of imperfect groups apparently began in. 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.
dcterms:subject
dbc:Properties_of_groups
dbo:wikiPageID
4939209
dbo:wikiPageRevisionID
1032040243
dbo:wikiPageWikiLink
dbr:Subgroup dbr:Subnormal_subgroup dbr:Group_theory dbr:Quotient_group dbc:Properties_of_groups dbr:Perfect_group dbr:Symmetric_group dbr:Direct_product_of_groups dbr:Solvable_group dbr:Group_(mathematics) dbr:Journal_of_Pure_and_Applied_Algebra dbr:Mathematics dbr:General_linear_group dbr:Wreath_product dbr:Group_extension dbr:Carter_subgroup dbr:Springer-Verlag dbr:Algebra
owl:sameAs
yago-res:Imperfect_group wikidata:Q6006292 n11:4nVAG freebase:m.0cw43m
dbp:wikiPageUsesTemplate
dbt:Abstract-algebra-stub dbt:Citation dbt:Harv dbt:Refimprove
dbo: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. The study of imperfect groups apparently began in. 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).
prov:wasDerivedFrom
wikipedia-en:Imperfect_group?oldid=1032040243&ns=0
dbo:wikiPageLength
2196
foaf:isPrimaryTopicOf
wikipedia-en:Imperfect_group
Subject Item
wikipedia-en:Imperfect_group
foaf:primaryTopic
dbr:Imperfect_group