The Engel elements in generalized FC-groups
نویسندگان
چکیده
منابع مشابه
Left 3-engel Elements in Groups
In this paper we study left 3-Engel elements in groups. In particular, we prove that for any prime p and any left 3-Engel element x of finite p-power order in a group G, x is in the Baer radical of G. Also it is proved that 〈x, y〉 is nilpotent of class 4 for every two left 3-Engel elements in a group G.
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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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Minimal non-FC-groups have been largely investigated and their structure is well-known. Minimal non-CC-groups, a first generalization of minimal non-FC-groups, have been investigated more recently and their complete description is still unknown. The present paper deals with generalizations of the notion of minimal non-FC-group in the context of locally nilpotent and locally solvable groups.
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A relationship between two natural dynamical systems on groups is established thereby giving a new characterization of Engel elements. Using this connection, various closure properties for the sets of left and right Engel elements are established. Some other dynamical systems and their relationship with Engel elements and nilpotency for finite groups are also considered.
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2014
ISSN: 0019-2082
DOI: 10.1215/ijm/1436275499