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Results 1 – 36    (Previous 50 | Next 50)   (20 | 50 | 100 | 250 | 500)   (JSON | CSV | RSS | RDF)
 Difficulty levelFact about
Abelian Frattini subgroup implies centralizer is criticalFrattini subgroup (?)
Abelian group (?)
Critical subgroup (?)
C-closed critical subgroup (?)
Abelian and abelian automorphism group not implies locally cyclicAbelian group (3)
Group whose automorphism group is abelian (2)
Locally cyclic group (2)
Abelian and ambivalent iff elementary abelian 2-groupAbelian group (3)
Ambivalent group (2)
Elementary abelian 2-group (3)
Abelian automorphism group not implies abelianGroup whose automorphism group is abelian (2)
Abelian group (2)
Abelian implies every element is automorphic to its inverseAbelian group (2)
Group in which every element is automorphic to its inverse (2)
Abelian implies every subgroup is potentially characteristicAbelian group (?)
Subgroup (?)
Potentially characteristic subgroup (?)
Subgroup of abelian group (2)
Potentially characteristic subgroup of abelian group (3)
Abelian implies nilpotentAbelian group (2)
Nilpotent group (2)
Abelian implies self-centralizing in holomorphAbelian group (2)
NSCFN-realizable group (2)
Holomorph of a group (?)
Self-centralizing subgroup (?)
NSCFN-subgroup (?)
NSCFN-realizable group (?)
Abelian normal is not join-closedAbelian normal subgroup (1)
Join-closed subgroup property (2)
Abelian group (1)
Normal join-closed group property (2)
Abelianness is 2-localAbelian group (1)
2-local group property (2)
Abelianness is directed union-closedAbelian group (1)
Directed union-closed group property (2)
Abelianness is quotient-closedAbelian group (1)
Quotient-closed group property (2)
Abelianness is subgroup-closedAbelian group (1)
Subgroup-closed group property (2)
CA not implies nilpotentCA-group (2)
Nilpotent group (2)
CN-group (2)
Abelian group (3)
Characteristic subgroup of abelian group not implies divisibility-closedCharacteristic subgroup of abelian group (2)
Divisibility-closed subgroup (2)
Abelian group (2)
Characteristic subgroup (2)
Characteristic subgroup of abelian group not implies local powering-invariantCharacteristic subgroup of abelian group (2)
Local powering-invariant subgroup (2)
Abelian group (2)
Characteristic subgroup (2)
Characteristic subgroup of uniquely p-divisible abelian group is uniquely p-divisibleAbelian group (?)
Characteristic subgroup (?)
Powered group for a set of primes (?)
Commuting fraction more than five-eighths implies abelianCommuting fraction (2)
Finite abelian group (?)
Number of conjugacy classes (2)
FZ-group (2)
Abelian group (3)
Cube map is endomorphism iff abelian (if order is not a multiple of 3)3Cube map (?)
Abelian group (?)
Cyclic automorphism group implies abelianGroup whose automorphism group is cyclic (?)
Automorphism group of a group (?)
Cyclic group (?)
Abelian group (?)
Cyclic implies abelianCyclic group (2)
Abelian group (2)
Dedekind not implies abelianDedekind group (2)
Abelian group (2)
Exponent two implies abelianExponent of a group (2)
Abelian group (3)
Elementary abelian group (2)
Finite abelian and abelian automorphism group implies cyclicFinite abelian group (3)
Group whose automorphism group is abelian (2)
Abelian group (3)
Cyclic group (3)
Finite cyclic groupl3 (?)
Finite abelian implies same orbit sizes of conjugacy classes and irreducible representations under automorphism groupFinite abelian group (2)
Finite group having the same orbit sizes of conjugacy classes and irreducible representations under automorphism group (2)
Finite abelian group (?)
Abelian group (?)
Full invariance is not direct power-closedFully invariant subgroup (1)
Direct power-closed subgroup property (2)
Abelian group (?)
Fully invariant not implies abelian-potentially verbal in abelian groupAbelian group (2)
Fully invariant subgroup (2)
Abelian-potentially verbal subgroup (2)
Fully invariant subgroup of abelian group not implies divisibility-closedFully invariant subgroup of abelian group (2)
Divisibility-closed subgroup (2)
Abelian group (2)
Fully invariant subgroup (2)
Intermediately characteristic not implies isomorph-containing in abelian groupAbelian group (2)
Intermediately characteristic subgroup (2)
Isomorph-containing subgroup (2)
Nilpotent not implies abelianNilpotent group (2)
Abelian group (2)
Nonempty characteristic subsemigroup of abelian group implies subgroupAbelian group (3)
Characteristic subgroup (3)
Quotients of elementarily equivalent abelian groups by multiples of n are elementarily equivalentAbelian group (?)
Elementarily equivalent groups (?)
Rational and abelian implies elementary abelian 2-groupRational group (2)
Abelian group (3)
There exist abelian groups whose isomorphism classes of direct powers have any given periodGroup isomorphic to its cube (2)
Group isomorphic to its square (2)
Torsion-free abelian group (?)
Abelian group (?)
Torsion-free group (?)
Direct power of a group (?)
Isomorphic groups (?)
Group isomorphic to its cube (?)
Group isomorphic to its square (?)
Torsion subgroups of elementary equivalent abelian groups are elementarily equivalentAbelian group (?)
Elementarily equivalent groups (?)
Torsion subgroup (?)
Verbal subgroup of abelian group not implies local powering-invariantVerbal subgroup of abelian group (2)
Local powering-invariant subgroup (2)
Abelian group (2)
Verbal subgroup (2)