Class groups of cyclic groups of square-free order
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- by Andrew Matchett PDF
- Trans. Amer. Math. Soc. 264 (1981), 251-254 Request permission
Abstract:
Let $G$ be a finite cyclic group of square free order. Let ${\text {Cl(}}ZG{\text {)}}$ denote the projective class group of the integral group ring $ZG$. Our main theorem describes explicitly the quotients of a certain filtration of ${\text {Cl(}}ZG{\text {)}}$. The description is in terms of class groups and unit groups of the rings of cyclotomic integers involved in $ZG$. The proof is based on a Mayer-Vietoris sequence.References
- A. Fröhlich, Locally free modules over arithmetic orders, J. Reine Angew. Math. 274(275) (1975), 112–124. MR 376619, DOI 10.1515/crll.1975.274-275.112
- John Milnor, Introduction to algebraic $K$-theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. MR 0349811
- I. Reiner and S. Ullom, A Mayer-Vietoris sequence for class groups, J. Algebra 31 (1974), 305–342. MR 349828, DOI 10.1016/0021-8693(74)90072-6
Additional Information
- © Copyright 1981 American Mathematical Society
- 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