On locally graded groups with a word whose values are Engel
نویسندگان
چکیده
منابع مشابه
On Groups admitting a Word whose Values are Engel
Let m,n be positive integers, v a multilinear commutator word and w = vm. We prove that if G is a residually finite group in which all wvalues are n-Engel, then the verbal subgroup w(G) is locally nilpotent. We also examine the question whether this is true in the case where G is locally graded rather than residually finite. We answer the question affirmatively in the case where m = 1. Moreover...
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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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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2015
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091515000152