منابع مشابه
4-Engel Groups are Locally Nilpotent
Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.
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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 کاملNilpotent Groups
The articles [2], [3], [4], [6], [7], [5], [8], [9], [10], and [1] provide the notation and terminology for this paper. For simplicity, we use the following convention: x is a set, G is a group, A, B, H, H1, H2 are subgroups of G, a, b, c are elements of G, F is a finite sequence of elements of the carrier of G, and i, j are elements of N. One can prove the following propositions: (1) ab = a · ...
متن کاملComputing 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 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...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1999
ISSN: 0263-6115
DOI: 10.1017/s144678870000118x