Computing with 4-engel Groups
نویسندگان
چکیده
We have proved that 4-Engel groups are locally nilpotent. The proof is based upon detailed computations by both hand and machine. Here we elaborate on explicit computer calculations which provided some of the motivation behind the proof. In particular we give details on the hardest coset enumerations now required to show in a direct proof that 4-Engel p-groups are locally finite for 5 ≤ p ≤ 31. We provide a theoretical result which enables us to do requisite coset enumerations much better and we also give a new, tight bound on the class of 4-Engel 5-groups. In addition we give further information on use of the Knuth-Bendix procedure for verifying nilpotency of a finitely presented group.
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