Class groups of cyclic groups of square-free order

Author:
Andrew Matchett

Journal:
Trans. Amer. Math. Soc. **264** (1981), 251-254

MSC:
Primary 13D15; Secondary 16A26, 20C10

MathSciNet review:
597880

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Abstract: Let be a finite cyclic group of square free order. Let denote the projective class group of the integral group ring . Our main theorem describes explicitly the quotients of a certain filtration of . The description is in terms of class groups and unit groups of the rings of cyclotomic integers involved in . The proof is based on a Mayer-Vietoris sequence.

**[1]**A. Fröhlich,*Locally free modules over arithmetic orders*, J. Reine Angew. Math.**274/275**(1975), 112–124. Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, III. MR**0376619****[2]**John Milnor,*Introduction to algebraic 𝐾-theory*, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. Annals of Mathematics Studies, No. 72. MR**0349811****[3]**I. Reiner and S. Ullom,*A Mayer-Vietoris sequence for class groups*, J. Algebra**31**(1974), 305–342. MR**0349828**

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DOI:
https://doi.org/10.1090/S0002-9947-1981-0597880-9

Article copyright:
© Copyright 1981
American Mathematical Society