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All partial sum values of squares of degrees of irreducible representations divide the order of the group for groups up to prime-fifth order, Alperin's fusion theorem in terms of well-placed tame intersections, Alternating implies flexible, Alternative implies powers up to the fifth are well-defined, Amalgam-characteristic implies image-potentially characteristic, Amalgam-characteristic implies potentially characteristic, Ambivalence is direct product-closed, Ambivalence is quotient-closed, Ambivalent not implies strongly ambivalent, Analogue of Thompson transitivity theorem fails for abelian subgroups of rank two, Analogue of Thompson transitivity theorem fails for groups in which not every p-local subgroup is p-constrained, Any abelian normal subgroup normalizes an abelian subgroup of maximum order, Any class two normal subgroup whose derived subgroup is in the ZJ-subgroup normalizes an abelian subgroup of maximum order, Artinian implies co-Hopfian, Artinian implies periodic, Ascendant not implies subnormal, Ascending chain condition on normal subgroups implies Hopfian, Ascending chain condition on subnormal subgroups implies subnormal join property, Ascending chain condition on subnormal subgroups is normal subgroup-closed, Associative implies generalized associative, At most n elements of order dividing n implies every finite subgroup is cyclic, Automorph-conjugacy is centralizer-closed, Automorph-conjugacy is normalizer-closed, Automorph-conjugacy is not finite-conjugate-intersection-closed, Automorph-conjugacy is not finite-intersection-closed, Automorph-conjugacy is not finite-join-closed, Automorph-conjugacy is transitive, Automorph-permutable not implies permutable, Automorphism group is transitive on non-identity elements implies characteristically simple, Baer Lie property is not quotient-closed, Baer Lie property is not subgroup-closed, Base of a wreath product implies right-transitively 2-subnormal, Base of a wreath product implies right-transitively conjugate-permutable, Base of a wreath product implies subset-conjugacy-closed, Base of a wreath product is transitive, Base of a wreath product not implies elliptic, Brauer's induction theorem, Brauer-Fowler inequality relating number of conjugacy classes of strongly real elements and number of involutions, Brauer-Fowler theorem on existence of subgroup of order greater than the cube root of the group order, Bryant-Kovacs theorem, Burnside's basis theorem, Burnside's theorem on coprime automorphisms and Frattini subgroup, C-closed implies local powering-invariant, C-closed implies powering-invariant, CA not implies nilpotent, CDIN of conjugacy-closed implies CDIN, CEP implies every relatively normal subgroup is weakly closed, Cayley's theorem, Center is normality-large implies every nontrivial normal subgroup contains a cyclic normal subgroup, Center of pronormal implies SCDIN