منابع مشابه
Computing with 4-engel Groups
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....
متن کاملRobert Fitzgerald Morse: Solvable Engel Groups 1 Solvable Engel Groups with Nilpotent Normal Closures
In this paper we investigate certain solvable (n+1)-Engel groups and bounded left Engel groups. We show that these (n + 1)-Engel groups can be characterized as those groups in which the normal closure of each element in the group is nilpotent of class at most n. Similarly, the bounded left Engel groups investigated can be characterized as those groups in which the normal closure of each element...
متن کاملun 2 00 4 Notes on Engel groups and Engel elements in groups . Some generalizations
Engel groups and Engel elements became popular in 50s. We consider in the paper the more general nil-groups and nil-elements in groups. All these notions are related to nilpotent groups and nilpo-tent radicals in groups. These notions generate problems which are parallel to Burnside problems for periodic groups. The first three theorems of the paper are devoted to nil-groups and Engel groups, w...
متن کاملGroup Rings with Solvable «-engel Unit Groups'
Let KG be the group ring of a group G over a field of characteristic p > 0, p ^ 2, 3. Suppose G contains no element of order p (if p > 0). Group algebras KG with unit group U(KG) solvable and n-Engel are characterized. Let ATG be the group ring of a group G over a field K of characteristic p > 0 and let U(KG) denote its group of units. Several authors including Bateman [1], Bateman and Coleman ...
متن کاملA Note on The Local Nilpotence of 4-Engel Groups
Recently Havas and Vaughan-Lee proved that 4-Engel groups are locally nilpotent. Their proof relies on the fact that a certain 4-Engel group T is nilpotent and this they prove using a computer and the Knuth-Bendix algorithm. In this paper we give a short hand-proof of the nilpotency of T .
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1983
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700026150