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The query [[uses::<q>[[Group acts as automorphisms by conjugation]] || [[uses::Group acts as automorphisms by conjugation]]</q>]] was answered by the SMWSQLStore3 in 0.0105 seconds.


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2-subnormal subgroup has a unique fastest ascending subnormal series
Abelian automorphism group implies class two
Analogue of critical subgroup theorem for infinite abelian-by-nilpotent p-groups
Center is local powering-invariant
Center is quotient-local powering-invariant in nilpotent group
Center is quotient-powering-invariant
Center of binary von Dyck group has order two
Centerless and characteristic in automorphism group implies automorphism group is complete
Centerless implies inner automorphism group is centralizer-free in automorphism group
Characteristic implies normal
Characteristic subalgebras are ideals in the variety of groups
Characterization of exponent semigroup of a finite p-group
Class equation of a group relative to a prime power
Commensurator of subgroup is subgroup
Cube map is endomorphism iff abelian (if order is not a multiple of 3)
Cube map is surjective endomorphism implies abelian
Cyclic automorphism group implies abelian
Equivalence of definitions of LUCS-Baer Lie group
Equivalence of definitions of finite characteristically simple group
Equivalence of definitions of intermediately subnormal-to-normal subgroup
Equivalence of definitions of universal congruence condition
Equivalence of normality and characteristicity conditions for conjugacy functor
Equivalence of normality and characteristicity conditions for isomorph-free p-functor
Equivalence of presentations of dicyclic group
Finite and any two maximal subgroups intersect trivially implies not simple non-abelian
Finite and cyclic automorphism group implies cyclic
Finite group having at least two conjugacy classes of involutions has order less than the cube of the maximum of orders of centralizers of involutions
Finite non-abelian and every proper subgroup is abelian implies not simple
Finite non-nilpotent and every proper subgroup is nilpotent implies not simple
Frattini subgroup of finite group is quotient-coprime automorphism-faithful
Group acts on set of subgroups by conjugation
Isoclinic groups have same proportions of conjugacy class sizes
Left coset space of centralizer is in bijective correspondence with conjugacy class
Local powering-invariance is not quotient-transitive in solvable group
N-abelian iff abelian (if order is relatively prime to n(n-1))
N-abelian implies every nth power and (n-1)th power commute
N-abelian implies n(n-1)-central
Nilpotent automorphism group implies nilpotent of class at most one more
Normal equals potentially characteristic
Normality is strongly join-closed
Nth power map is surjective endomorphism implies (n-1)th power map is endomorphism taking values in the center
Number of nth roots of any conjugacy class is a multiple of n
Pi-separable and pi'-core-free implies pi-core is self-centralizing
Quotient-powering-invariance is union-closed
Size of conjugacy class divides index of center
Size of conjugacy class divides order of group
Size of conjugacy class of subgroups equals index of normalizer
Solvable automorphism group implies solvable of derived length at most one more
Sylow number equals index of Sylow normalizer
There are finitely many finite groups with bounded number of conjugacy classes