# Semantic search

Center not is intermediately local powering-invariant in solvable group, Center not is quotient-local powering-invariant in solvable group, Characteristic not implies powering-invariant in solvable group, Classification of solvable transitive subgroups of symmetric group of prime degree, Core-free permutable subnormal implies solvable of length at most one less than subnormal depth, Derived length is logarithmically bounded by nilpotency class, Every finite non-solvable group has a minimal simple group as subquotient, Finite N-group is solvable or almost simple, Hall's theorem, Imperfect not implies hypoabelian, Isoclinic groups have same derived length, Maximal normal iff normal of prime index in solvable, Minimal normal implies additive group of a field in solvable group, Minimal normal implies powering-invariant in solvable group, N-group not implies solvable or minimal simple, Odd-order and CN implies solvable, Odd-order implies solvable, Orbital maximin equals number of ordered pairs of distinct elements for solvable groups iff size is prime power, Order has only two prime factors implies solvable, Schmidt-Iwasawa theorem, Second center not is local powering-invariant in solvable group, Socle is powering-invariant in solvable group, Solvability is 2-local for finite groups, Solvability is extension-closed, Solvability is subgroup-closed, Solvable automorphism group implies solvable of derived length at most one more, Solvable implies Fitting subgroup is self-centralizing, Solvable not implies nilpotent, Solvable not implies solvable automorphism group, Square-free implies solvability-forcing