A group element is called a generalized torsion element if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the generalized order of an element in a finite group G using its character table.

中文翻译：

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成组的广义扭转单元

如果群元素的共轭有限积等于恒等式，则群元素称为广义扭转元素。我们证明，在幂零群或 FC 群中，广义扭转单元都是扭转单元。此外，我们使用其字符表计算有限群G中元素的广义阶。