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A-group, Abelian group, Ambivalent group, Amenable discrete group, Cyclic group, Cyclic group of prime power order, Dedekind group, FC-group, Finite abelian group, Finite cyclic group, Finite group, Finite group having a subgroup series with prime indexes, Finite group with periodic cohomology, Finite nilpotent group, Finite supersolvable group, Finitely generated abelian group, Finitely generated group, Frattini-free group, Group generated by involutions, Group in which any two elements generating the same cyclic subgroup are automorphic, Group satisfying a nontrivial identity, Group satisfying normalizer condition, Group with finite derived subgroup, J-group, K-group, Locally cyclic group, Locally finite group, Locally nilpotent group, Metabelian group, Nilpotent group, Noetherian group, Perfect group, Periodic group, Polycyclic group, Rational group, Regular p-group, Semisimple group, Solvable group, Supersolvable group, T*-group, T-group, Z-group