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On residually finite groups satisfying an Engel type identity
Monatshefte für Mathematik ( IF 0.8 ) Pub Date : 2020-02-18 , DOI: 10.1007/s00605-020-01390-y
Danilo Silveira

Let $ n, q $ be positive integers. We show that if $ G $ is a finitely generated residually finite group satisfying the identity $ [x,_ny^q]\equiv 1, $ then there exists a function $ f(n) $ such that $ G $ has a nilpotent subgroup of finite index of class at most $ f(n) $. We also extend this result to locally graded groups.

中文翻译:

关于满足 Engel 类型恒等式的残差有限群

令 $n, q $ 为正整数。我们证明如果 $ G $ 是一个满足恒等式 $ [x,_ny^q]\equiv 1, $ 的有限生成残差有限群,那么存在一个函数 $ f(n) $ 使得 $ G $ 有一个幂零子群类的有限索引至多 $ f(n) $。我们还将此结果扩展到本地评分组。
更新日期:2020-02-18
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