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Class Groups of Cyclic Groups of Square Free Order

Andrew Matchett
Transactions of the American Mathematical Society
Vol. 264, No. 1 (Mar., 1981), pp. 251-254
DOI: 10.2307/1998423
Stable URL: http://www.jstor.org/stable/1998423
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Class Groups of Cyclic Groups of Square Free Order
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Abstract

Let $G$ be a finite cyclic group of square free order. Let $\operatorname{Cl}(ZG)$ denote the projective class group of the integral group ring $ZG$. Our main theorem describes explicitly the quotients of a certain filtration of $\operatorname{Cl}(ZG)$. 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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