CN-group (original) (raw)
In mathematics, in the area of algebra known as group theory, a more than fifty-year effort was made to answer a conjecture of: are all groups of odd order solvable? Progress was made by showing that CA-groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvable. Further progress was made showing that CN-groups, groups in which the centralizer of a non-identity element is nilpotent, of odd order are solvable. The complete solution was given in, but further work on CN-groups was done in, giving more detailed information about the structure of these groups. For instance, a non-solvable CN-group G is such that its largest solvable normal subgroup O∞(G) is a 2-group, and the quotient is a group of even order.
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| dbo:abstract | In mathematics, in the area of algebra known as group theory, a more than fifty-year effort was made to answer a conjecture of: are all groups of odd order solvable? Progress was made by showing that CA-groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvable. Further progress was made showing that CN-groups, groups in which the centralizer of a non-identity element is nilpotent, of odd order are solvable. The complete solution was given in, but further work on CN-groups was done in, giving more detailed information about the structure of these groups. For instance, a non-solvable CN-group G is such that its largest solvable normal subgroup O∞(G) is a 2-group, and the quotient is a group of even order. (en) |
| dbo:wikiPageExternalLink | http://projecteuclid.org/Dienst/UI/1.0/Journal%3Fauthority=euclid.pjm&issue=1103053941 |
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| dbo:wikiPageRevisionID | 1123406923 (xsd:integer) |
| dbo:wikiPageWikiLink | dbc:Group_theory dbr:Mathematics dbr:Mathematische_Zeitschrift dbc:Properties_of_groups dbr:Core_(group) dbr:Algebra dbr:3-step_group dbc:Finite_groups dbr:Nilpotent_group dbr:Group_(mathematics) dbr:CA-group dbr:Group_theory dbr:Mersenne_prime dbr:Order_(group_theory) dbr:Solvable_group dbr:P-group dbr:Fermat_prime dbr:Transactions_of_the_American_Mathematical_Society dbr:Frobenius_groups dbr:Centralizer dbr:Suzuki_simple_group |
| dbp:wikiPageUsesTemplate | dbt:About dbt:Citation dbt:Harv dbt:Harvid dbt:Abstract-algebra-stub |
| dcterms:subject | dbc:Group_theory dbc:Properties_of_groups dbc:Finite_groups |
| rdf:type | yago:Abstraction100002137 yago:Group100031264 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 yago:WikicatFiniteGroups yago:WikicatPropertiesOfGroups |
| rdfs:comment | In mathematics, in the area of algebra known as group theory, a more than fifty-year effort was made to answer a conjecture of: are all groups of odd order solvable? Progress was made by showing that CA-groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvable. Further progress was made showing that CN-groups, groups in which the centralizer of a non-identity element is nilpotent, of odd order are solvable. The complete solution was given in, but further work on CN-groups was done in, giving more detailed information about the structure of these groups. For instance, a non-solvable CN-group G is such that its largest solvable normal subgroup O∞(G) is a 2-group, and the quotient is a group of even order. (en) |
| rdfs:label | CN-group (en) |
| owl:sameAs | freebase:CN-group yago-res:CN-group wikidata:CN-group https://global.dbpedia.org/id/4e3wC |
| prov:wasDerivedFrom | wikipedia-en:CN-group?oldid=1123406923&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:CN-group |
| is dbo:wikiPageRedirects of | dbr:CN_group |
| is dbo:wikiPageWikiLink of | dbr:CA-group dbr:Suzuki_groups dbr:CN_group |
| is foaf:primaryTopic of | wikipedia-en:CN-group |