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2-subnormal implies join-transitively subnormal
ACIC is characteristic subgroup-closed
Artin's induction theorem
Ascending chain condition on subnormal subgroups implies subnormal join property
Automorph-conjugacy is transitive
Automorphism sends more than three-fourths of elements to inverses implies abelian
Cartan-Brauer-Hua theorem
Central implies normal satisfying the subgroup-to-quotient powering-invariance implication
Centralizer product theorem
Characteristic of normal implies normal
Characteristicity is transitive
Classification of groups of prime-cube order
Classification of groups of prime-square order
Commensurator of subgroup is subgroup
Commuting of non-identity elements defines an equivalence relation between prime divisors of the order of a finite CN-group
Complemented normal implies quotient-powering-invariant
Congruence condition on index of subgroup containing Sylow-normalizer
Conjugacy class of elements with semisimple generalized Jordan block does not split in special linear group over a finite field
Conjugacy class of prime power size implies not simple
Corollary of centralizer product theorem for rank at least three
Cube map is surjective endomorphism implies abelian
Degree of irreducible representation divides index of abelian normal subgroup
Degree of irreducible representation divides order of group
Derived subgroup satisfies ascending chain condition on subnormal subgroups implies subnormal join property
Endomorphism kernel implies quotient-powering-invariant
Endomorphism sends more than three-fourths of elements to squares implies abelian
Equivalence of definitions of gyrogroup
Every finite division ring is a field
Finite and any two maximal subgroups intersect trivially implies not simple non-abelian
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 metabelian
Finite non-abelian and every proper subgroup is abelian implies not simple
Finite non-nilpotent and every proper subgroup is nilpotent implies not simple
Finite supersolvable implies subgroups of all orders dividing the group order
Finitely generated and residually finite implies Hopfian
Fixed-point-free involution on finite group is inverse map
Frattini-in-center odd-order p-group implies (mp plus 1)-power map is automorphism
Frattini-in-center odd-order p-group implies p-power map is endomorphism
Hypoabelian not implies imperfect
Infinite group with cofinite topology is not a topological group
Isoclinic groups have same nilpotency class
Isoclinic groups have same proportions of conjugacy class sizes
Linear representation is realizable over principal ideal domain iff it is realizable over field of fractions
Local finiteness is extension-closed
Monomorphism iff injective in the category of groups
Nilpotent Hall subgroups of same order are conjugate
Normal equals potentially characteristic
Normal of finite index implies completely divisibility-closed
Normal of finite index implies quotient-powering-invariant
Normal subgroup contained in the hypercenter satisfies the subgroup-to-quotient powering-invariance implication
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