Let G be a nonabelian nilpotent group and F a field of characteristic p > 2, such that the unit group \(\mathcal {U}(FG)\) of the group ring FG is solvable and G contains a p-element. Here we provide a lower bound for the derived length of \(\mathcal {U}(FG)\) that corrects the result from Lee et al. (Algebr. Represent. Theory 17, 1597–1601 2014) when G is nontorsion and \(G^{\prime }\) is a finite p-group.

中文翻译：

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关于非扭转群代数的单位群导出长度的下界

令G为一个非阿贝拉幂子群，F为特征p > 2的场，使得基环FG的单元群\（\ mathcal {U}（FG）\）是可解的，并且G包含p元素。在这里，我们为\（\ mathcal {U}（FG）\）的导出长度提供了一个下限，该下限纠正了Lee等人的结果。（Algebr。代表理论17，1697至01年2014）当G ^是nontorsion和\（G ^ {\素} \）是一个有限p -基团。