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Transactions of the American Mathematical Society
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
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0597880-9
PII: S 0002-9947(1981)0597880-9
Article copyright: © Copyright 1981 American Mathematical Society