On groups in which Engel sinks are cyclic
نویسندگان
چکیده
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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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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Similar kinds of problems have often been object of investigation. For instance, in [5] Fitzpatrick, using the classification of finite simple groups, proved that if in a finite group G any two elements of the same order are conjugate, thenG is isomorphic with the symmetric group Sn, with n ∈ {1, 2, 3} (see also [4]). Then in [10] there is the classification of finite groups for which elements ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2019
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.08.019