Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 13D15, 16A26, 20C10

Retrieve articles in all journals with MSC: 13D15, 16A26, 20C10

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society