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Let F be a field and G a group. We present the classical results determining the conditions under which \(\mathcal {U}(FG)\) is a nilpotent group. Assuming that char \(F\ne 2\) , we then discuss more recent results determining when the set of symmetric units, \(\mathcal {U}^+(FG)\) , is nilpotent. If F is infinite and G is torsion, then we can allow the involution to be arbitrary. Otherwise, we work with the classical involution.

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Nilpotence of \(\mathcal {U} (FG)\) and \(\mathcal {U}^+(FG)\)

  • 章节

  • 发表日期：

    2025年

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  • Gregory T. Lee

摘要

Let F be a field and G a group. We present the classical results determining the conditions under which \(\mathcal {U}(FG)\) is a nilpotent group. Assuming that char \(F\ne 2\) , we then discuss more recent results determining when the set of symmetric units, \(\mathcal {U}^+(FG)\) , is nilpotent. If F is infinite and G is torsion, then we can allow the involution to be arbitrary. Otherwise, we work with the classical involution.