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

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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.