Mathematical Sciences: The Induction Exponent e of an Infinite Discrete Group

本课题主要研究从群G到正规整环的虚Hattori-Stallings秩函数。证明了这样的函数是G的有限超初等子群的诱导和。这将推广已知的线性群的情形。这项研究是关于高K理论在群环的具体问题上的应用。如果主要结果成立，它将暗示Bass的强猜想，并将证明Goldie秩猜想和零因子猜想的陈述对特征为零的所有Goldie群环都成立。

This project is concerned with virtual Hattori-Stallings rank functions from a group G to a normal domain. It will be shown that such a function is a sum of inductions from finite hyperelementary subgroups of G. This will extend the known situation for linear groups. The research is concerned with applications of higher K- theory to concrete problems about group rings. If the main result is established, it will imply Bass' Strong conjecture and will show that the statements of the Goldie rank conjecture and zero divisor conjecture hold for all Goldie group rings in charateristic zero.