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

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

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. MR**0376619 (51:12794)****[2]**J. Milnor,*Introduction to algebraic**-theory*, Ann. of Math. Studies, no. 72, Princeton Univ. Press, Princeton, N. J., 1971. MR**0349811 (50:2304)****[3]**I. Reiner and S. Ullom,*A Mayer-Vietoris sequence for class groups*, J. Algebra**31**(1974), 305-342. MR**0349828 (50:2321)**

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

Article copyright:
© Copyright 1981
American Mathematical Society