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11.123 (1990)

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(Well-known problem). For a given group $G$, define the following sequence of groups: $A_1(G) = G, \ A_{i+1}(G) = \operatorname{Aut}(A_i(G))$. Does there exist a finite group $G$ for which this sequence contains infinitely many non-isomorphic groups?

Contributor: M. Short

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