Locally Finite Groups

abelian group abelian normal subgroup assumption Cernikov group Clearly conjugacy class consisting of finite contradiction Corollary counter example denote dihedral element g element of G element x e elementary abelian embedding exists an element F of odd factor group field F finite group satisfying finite index finite simple groups finite subgroups Frobenius complement Frobenius group functor G is isomorphic G satisfies GL(n Hence homomorphism index in G intersection inverse limit involution involution of G isomorphic isomorphic to PSL(2 Lemma Let G linear group locally finite field locally finite group locally finite simple locally nilpotent locally nilpotent group locally soluble group maximal p-subgroups minimal condition natural number non-empty odd characteristic p-group periodic group Proof proper subgroup Prüfer regular cardinal result satisfying the minimal sequence subgroup H subgroup of finite subgroup of G subset Sunkov Sylow p-subgroup symmetric group system of G Theorem universal group