整群环上投射模的消去性质
The cancellation property for projective modules over integral group rings
AI总结：
本文部分分类了使整群环具有投射消去性的有限群，基于 Eichler 条件的相对版本证明消去定理，并结合群论论证与前人结果确定了最终分类。
摘要：
我们获得了对有限群 $G$ 的部分分类，使得整群环 $\mathbb{Z} G$ 具有投射消去性，即对于投射 $\mathbb{Z} G$-模 $P$ 和 $Q$，$P \oplus \mathbb{Z} G \cong Q \oplus \mathbb{Z} G$ 意味着 $P \cong Q$。特别地，我们确定了没有例外二元多面体商的有限群何时满足投射消去性。为此，我们基于 Eichler 条件的相对版本证明了一个消去定理。然后，我们运用群论论证精确确定了未被此结果涵盖的群类。最终分类则是通过应用 Swan、Chen 及 Bley-Hofmann-Johnston 的结果得出，这些结果表明了某些群不满足投射消去性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
