There exists a finite E-group of nilpotency class three, answering Caranti's question recorded as Kourovka Notebook Problem 11.46(a).
Caranti,A module-theoretic approach to abelian automorphism groups, Israel J
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A Finite E-Group of Nilpotency Class Three
There exists a finite E-group of nilpotency class three, answering Caranti's question recorded as Kourovka Notebook Problem 11.46(a).