منابع مشابه
Some Engel Conditions on Finite Subsets of Certain Groups
Let nand k be positive integers. We say that a group G satisfies the condition £(n) (respectively, £dn)) if and only if any set with n + 1 elements of G contains two distinct elements x, y such that [x,t y] = 1 for some positive integer t = t(x, y) (respectively, [X,k y] = 1). Here we study certain groups satisfying these conditions. We prove that if G is a finite group satisfying the condition...
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 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 کاملEngel Conditions and Symmetric Tensors
In a recent study of Engel Lie rings, Serena Cicalò and Willem de Graaf have given a practical set of conditions for an additively finitely generated Lie ring L to satisfy an Engel condition. We present a simpler and more direct proof of this fact. Then we generalize it to a result in the language of tensor algebra, which can be applied to other contexts.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rendiconti del Circolo Matematico di Palermo Series 2
سال: 2020
ISSN: 0009-725X,1973-4409
DOI: 10.1007/s12215-020-00485-7