2023•Unpublished venueRequires access

On the Picard Group of the Integer Group Ring of the Cyclic p-Group and of Rings Close to It

Alexander Stolin

Abstract

It is proved that Clℤ [ ζ n ] is a direct summand of Pic (ℤ[ C p n ]), where p is an odd prime number, https://www.w3.org/1998/Math/MathML" display="inline"> ζ n p n = 1 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003421924/681b618c-53a0-438b-aca7-e7d50ecf07a1/content/eq2454.tif "/> and C p n is the cyclic group of order p n .

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Key concepts: Cyclic group, Mathematics, Group (periodic table), Order (exchange), Group ring, Prime (order theory), Ring (chemistry), Integer (computer science)