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Results 1 – 35    (Previous 50 | Next 50)   (20 | 50 | 100 | 250 | 500)   (JSON | CSV | RSS | RDF)
 Difficulty levelFact about
Automorphism group of finitary symmetric group equals symmetric groupSymmetric group (?)
Finitary symmetric group (?)
Classification of symmetric groups that are N-groupsSymmetric group (3)
N-group (3)
Conjugacy class of transpositions is the unique smallest conjugacy class of involutionsTransposition (?)
Symmetric group (?)
Conjugacy class (?)
Cycle type determines conjugacy classCycle type of a permutation (1)
Conjugate elements (2)
Symmetric group (3)
Conjugacy class (3)
Finitary alternating group is characteristic in symmetric groupAlternating group (?)
Characteristic subgroup (?)
Symmetric group (?)
Finitary alternating group is conjugacy-closed in symmetric groupAlternating group (?)
Conjugacy-closed subgroup (?)
Symmetric group (?)
Conjugacy-closed normal subgroup (?)
Finitary alternating group is intermediately monolith in symmetric groupAlternating group (?)
Monolith (?)
Symmetric group (?)
Finitary symmetric group equals center of symmetric group modulo finitary alternating groupSymmetric group (?)
Finitary symmetric group (?)
Alternating group (?)
Center (?)
Finitary symmetric group is automorphism-faithful in symmetric groupFinitary symmetric group (?)
Automorphism-faithful subgroup (?)
Symmetric group (?)
Finitary symmetric group is centralizer-free in symmetric groupFinitary symmetric group (?)
Centralizer-free subgroup (?)
Symmetric group (?)
Finitary symmetric group is characteristic in symmetric groupFinitary symmetric group (?)
Characteristic subgroup (?)
Symmetric group (?)
Finitary symmetric group is locally inner automorphism-balanced in symmetric groupFinitary symmetric group (?)
Locally inner automorphism-balanced subgroup (?)
Symmetric group (?)
Finitary symmetric group is normal in symmetric groupFinitary symmetric group (?)
Normal subgroup (?)
Symmetric group (?)
Finitary symmetric group is not fully invariant in symmetric groupFinitary symmetric group (?)
Fully invariant subgroup (?)
Symmetric group (?)
Isotropy of finite subset has finite double coset index in symmetric groupSubgroup of finite double coset index (?)
Symmetric group (?)
Number of conjugacy classes of subgroups in symmetric group is logarithmically bounded by square of degreeSymmetric group (?)
Symmetric group on finite set (?)
Subgroup rank of symmetric group is about half the degreeSymmetric group (3)
Subgroup rank of a group (2)
Symmetric group on a finite set is 2-generated2Symmetric group (?)
2-generated group (?)
Minimum size of generating set (?)
Symmetric group on a finite set is a Coxeter groupSymmetric group (?)
Coxeter group (?)
Symmetric group on finite or cofinite subset is conjugacy-closedConjugacy-closed subgroup (?)
Symmetric group (?)
Symmetric group on finite or cofinite subset is subset-conjugacy-closedSubset-conjugacy-closed subgroup (?)
Symmetric group (?)
Symmetric group on finite set has Sylow subgroup of prime orderSymmetric group (?)
Symmetric group on finite set (?)
Sylow subgroup (?)
Group of prime order (?)
Symmetric group on infinite coinfinite subset is not conjugacy-closedConjugacy-closed subgroup (?)
Symmetric group (?)
Symmetric groups are almost simpleSymmetric group (?)
Almost simple group (?)
Symmetric groups are ambivalentSymmetric group (?)
Ambivalent group (?)
Symmetric groups are normal-comparableSymmetric group (?)
Group in which any two normal subgroups are comparable (?)
Symmetric groups are rationalSymmetric group (?)
Rational group (?)
Symmetric groups are rational-representationSymmetric group (?)
Rational-representation group (?)
Symmetric groups are strongly ambivalentSymmetric group (?)
Strongly ambivalent group (?)
Strongly real element (?)
Symmetric groups on finite sets are completeSymmetric group (?)
Symmetric group on finite set (?)
Complete group (?)
Group in which every automorphism is inner (?)
Transposition-preserving automorphism of finitary symmetric group is induced by conjugation by a permutationSymmetric group (?)
Finitary symmetric group (?)
Transposition-preserving automorphism of symmetric group is innerSymmetric group (?)
Transposition (?)
Transpositions generate the finitary symmetric groupFinitary symmetric group (2)
Transposition (2)
Symmetric group (?)
Transposition (?)
Finitary symmetric group (?)
Transpositions of adjacent elements generate the symmetric group on a finite setTransposition (?)
Symmetric group (?)
Weakly normal subgroup of symmetric group must move more than half the elementsSymmetric group (?)
Weakly normal subgroup (?)
Pronormal subgroup (?)
Paranormal subgroup (?)
Polynormal subgroup (?)