标题： 投影模在整数群环上的消去性质 显示英文标题

标题： The cancellation property for projective modules over integral group rings

摘要： 我们获得了对有限群$G$的部分分类，这些群的整数群环$\mathbb{Z} G$具有投射消去性，即对于这些群，若$P \oplus \mathbb{Z} G \cong Q \oplus \mathbb{Z} G$则$P \cong Q$对于投射的$\mathbb{Z} G$-模$P$和$Q$成立。特别地，我们确定了当一个有限群没有异常二面体商时，投射消去性何时成立。为此，我们基于 Eichler 条件的一个相对版本证明了一个消去定理。然后我们使用一个群论论证来精确确定未被该结果覆盖的群类。最后通过应用 Swan、Chen 以及 Bley-Hofmann-Johnston 的结果得到最终分类，这些结果表明某些群的投射消去性失败。 显示英文摘要

摘要： We obtain a partial classification of the finite groups $G$ for which the integral group ring $\mathbb{Z} G$ has projective cancellation, i.e. for which $P \oplus \mathbb{Z} G \cong Q \oplus \mathbb{Z} G$ implies $P \cong Q$ for projective $\mathbb{Z} G$-modules $P$ and $Q$. In particular, we determine when projective cancellation holds for a finite group with no exceptional binary polyhedral quotients. To do this, we prove a cancellation theorem based on a relative version of the Eichler condition. We then use a group theoretic argument to precisely determine the class of groups not covered by this result. The final classification is then obtained by applying results of Swan, Chen and Bley-Hofmann-Johnston which show failure of projective cancellation for certain groups.