The local nilpotence theorem for 4-Engel groups revisited

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The proof of the local nilpotence theorem for 4-Engel groups was completed by G. Havas and M. Vaughan-Lee in 2005. The complete proof on the other hand is spread over several articles and the aim of this paper is to give a complete coherent linear version. In the process we are also able to make few simplifications and in particular we are able to merge two of the key steps into one.