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If $$A$$ A is a nontrivial torsion-free, locally cyclic group with no nontrivial divisible quotients, and $$G$$ G is the split extension of $$A$$ A by a group of order 2 acting on $$A$$ A by means of the inverting map, then $$G\simeq {{{\mathrm{Aut}}}G} $$ G ≃ Aut G . We prove that in no other case the full automorphism group of a group is infinite and...
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