We study \((\sigma ,\tau )\)-derivations of a group ring RG where G is a group with center having finite index in G and R is a semiprime ring with 1 such that either R has no torsion elements or that if R has p-torsion elements, then p does not divide the order of G and let \(\sigma ,\tau \) be R-linear endomorphisms of RG fixing the center of RG pointwise. We generalize Main Theorem 1.1 of Chaudhuri (Comm Algebra 47(9): 3800–3807, 2019) and prove that there is a ring \(T\supset R\) such that \(\mathcal {Z}(T)\supset \mathcal {Z}(R)\) and that for the natural extensions of \(\sigma , \tau \) to TG, we get \(H^1(TG,{}_\sigma TG_\tau )=0\), where \({}_\sigma TG_\tau \) is the twisted \(TG-TG\)-bimodule. We provide applications of the above result and Main Theorem 1.1 of Chaudhuri (2019) to integral group rings of finite groups and connect twisted derivations of integral group rings to other important problems in the field such as the isomorphism problem and the Zassenhaus conjectures. We also give an example of a group G which is both locally finite and nilpotent and such that for every field F, there exists an F-linear \(\sigma \)-derivation of FG which is not \(\sigma \)-inner.

我们研究\（（\ sigma，\ tau）\） -群环RG的派生，其中G是中心在G中具有有限索引的群，R是半素环，其R为1，因此R没有扭转元素或如果ř具有p -torsion元素，则p不分割的顺序ģ和让\（\西格玛，\ tau蛋白\） BE - [R的自同态-线性RG固定的中心RG逐点。我们推广Chaudhuri的主定理1.1（Comm Algebra 47（9）：3800-3807，2019）并证明存在一个环\（T \ supset R \）使得\（\ mathcal {Z}（T）\ supset \ mathcal {Z}（R）\）和\（\ sigma，\ tau \）到TG的自然扩展，我们得到\（H ^ 1（TG，{} _ \ sigma TG_ \ tau）= 0 \），其中\（{} _ \ sigma TG_ \ tau \）是扭曲的\（TG-TG \）- bimodule 。我们将上述结果和Chaudhuri（2019）的主定理1.1应用到有限群的整体群环上，并将整体群环的扭曲导数连接到该领域中的其他重要问题，例如同构问题和Zassenhaus猜想。我们还给出了一个G组的例子，它既是局部有限的又是幂零的，并且对于每个场F，存在FG的F线性\（\ sigma \） -导数，而不是\\\\ sigma \）内部。