exercise on group rings

From: Ignacio <ignat.soroko@xxxxxxxxx>
Date: Fri, 06 Jul 2007 17:50:18 -0700

Could you please help me with the following exercise:

Let G be a group and ZG its group algebra over integers. Also, let IG
be the augmentation ideal, i.e. the kernel of the homomorphism eps: ZG
--> G, mapping every element g to 1.

We need to prove that if IG is finitely generated as a left ideal,
then G is finitely generated.

Thank you!

.

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