ABSTRACT
Let G be a finite p-group and let https://www.w3.org/1998/Math/MathML"> A ( p G ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332630/bdf2b6ad-8ca8-4d57-9bb0-ce1a8aabf4d0/content/inline-math120.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> be the augmentation ideal of the group algebra https://www.w3.org/1998/Math/MathML"> p G https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332630/bdf2b6ad-8ca8-4d57-9bb0-ce1a8aabf4d0/content/inline-math121.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> over the field of p elements. Then https://www.w3.org/1998/Math/MathML"> V ( p G ) = 1 + A ( p G ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332630/bdf2b6ad-8ca8-4d57-9bb0-ce1a8aabf4d0/content/inline-math122.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is the group of normalized units of https://www.w3.org/1998/Math/MathML"> p G https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332630/bdf2b6ad-8ca8-4d57-9bb0-ce1a8aabf4d0/content/inline-math123.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
