Simple group
type: Ontology
creation date: 2025-12-04T12:39:51+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Simple group
type: Subject
type: Category:Semi-basic definitions in group theory
type: Category:Group properties
type: Category:Pivotal group properties
type: Category:GAP-testable group properties
type: Category:Standard terminology
page: https://groupprops.subwiki.org/wiki/Simple_group
wiki namespace: 0
wiki page content language: en
defining ingredient: Normal subgroup
defining ingredient: Subnormal subgroup
defining ingredient: Homomorphism of groups
defining ingredient: Trivial homomorphism of groups
defining ingredient: Simple group operator
importance rank: 2
obtained by applying: Simple group operator
page class: Term
stronger than: Monolithic group
stronger than: One-headed group
stronger than: Group of finite composition length
stronger than: Characteristically simple group
stronger than: Directly indecomposable group
stronger than: Centrally indecomposable group
stronger than: Splitting-simple group
stronger than: Primitive group
stronger than: Group satisfying ascending chain condition on subnormal subgroups
stronger than: Group satisfying ascending chain condition on normal subgroups
stronger than: Group in which every endomorphism is trivial or injective
stronger than: Hopfian group
weaker than: Simple non-abelian group
weaker than: Absolutely simple group
weaker than: Strictly simple group
weaker than: Finite simple group
weaker than: Finite simple non-abelian group
wiki page modification date: 2023-12-15T21:12:57Z
modification date#aux: 2460294.3839931
wiki page sort key: Simple group

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Cyclic group:Z73
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wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z73

Cyclic group:Z89
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ89
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z89

Cyclic group:Z11
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ11
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z11

Cyclic group:Z13
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ13
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z13

Cyclic group:Z17
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ17
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z17

Cyclic group:Z19
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ19
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z19

Cyclic group:Z23
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ23
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z23

Cyclic group:Z29
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ29
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z29

Cyclic group:Z31
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ31
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z31

Cyclic group:Z37
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ37
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z37

Cyclic group:Z41
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ41
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z41

Cyclic group:Z43
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ43
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z43

Cyclic group:Z47
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ47
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z47

Cyclic group:Z53
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ53
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z53

Cyclic group:Z59
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ59
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z59

Cyclic group:Z67
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ67
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z67

Cyclic group:Z79
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ79
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z79

Cyclic group:Z83
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ83
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Cyclic group:Z83

Dihedral group:D14
type: Subject
page: https://groupprops.subwiki.org/wiki/Dihedral_group-3AD14
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Dihedral group:D14

Dihedral group:D22
type: Subject
page: https://groupprops.subwiki.org/wiki/Dihedral_group-3AD22
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Dihedral group:D22

Dihedral group:D26
type: Subject
page: https://groupprops.subwiki.org/wiki/Dihedral_group-3AD26
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Dihedral group:D26

Projective special linear group:PSL(3,2)
type: Subject
page: https://groupprops.subwiki.org/wiki/Projective_special_linear_group-3APSL-283-2C2-29
wiki namespace: 0
wiki page content language: en
satisfies property: Simple group
wiki page sort key: Projective special linear group:PSL(3,2)

Satisfies property
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3ASatisfies_property
wiki namespace: 132
wiki page content language: en
wiki page sort key: Satisfies property
type: wpg