Quotientable automorphism (original) (raw)
In mathematics, in the realm of group theory, a quotientable automorphism of a group is an automorphism that takes every normal subgroup to within itself. As a result, it gives a corresponding automorphism for every quotient group. All are quotientable, and particularly, all class automorphisms and power automorphisms are. As well, all inner automorphisms are quotientable, and more generally, any automorphism defined by an algebraic formula is quotientable. * v * t * e
| Property | Value |
|---|---|
| dbo:abstract | In mathematics, in the realm of group theory, a quotientable automorphism of a group is an automorphism that takes every normal subgroup to within itself. As a result, it gives a corresponding automorphism for every quotient group. All are quotientable, and particularly, all class automorphisms and power automorphisms are. As well, all inner automorphisms are quotientable, and more generally, any automorphism defined by an algebraic formula is quotientable. * v * t * e (en) |
| dbo:wikiPageID | 5632598 (xsd:integer) |
| dbo:wikiPageLength | 631 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 606964440 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Power_automorphism dbr:Mathematics dbr:Normal_subgroup dbr:Quotient_group dbr:Group_automorphism dbc:Group_automorphisms dbr:Class_automorphism dbr:Group_theory dbr:Inner_automorphism dbr:Family_automorphism |
| dbp:wikiPageUsesTemplate | dbt:Algebra-stub dbt:Unreferenced |
| dct:subject | dbc:Group_automorphisms |
| gold:hypernym | dbr:Automorphism |
| rdfs:comment | In mathematics, in the realm of group theory, a quotientable automorphism of a group is an automorphism that takes every normal subgroup to within itself. As a result, it gives a corresponding automorphism for every quotient group. All are quotientable, and particularly, all class automorphisms and power automorphisms are. As well, all inner automorphisms are quotientable, and more generally, any automorphism defined by an algebraic formula is quotientable. * v * t * e (en) |
| rdfs:label | Quotientable automorphism (en) |
| owl:sameAs | freebase:Quotientable automorphism wikidata:Quotientable automorphism https://global.dbpedia.org/id/4tiY6 |
| prov:wasDerivedFrom | wikipedia-en:Quotientable_automorphism?oldid=606964440&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Quotientable_automorphism |
| is dbo:wikiPageWikiLink of | dbr:Class_automorphism |
| is foaf:primaryTopic of | wikipedia-en:Quotientable_automorphism |