Integral representations of cyclic groups of order $p^{2}$
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- by Irving Reiner PDF
- Proc. Amer. Math. Soc. 58 (1976), 8-12 Request permission
Erratum: Proc. Amer. Math. Soc. 63 (1977), 374.
Abstract:
Let $p$ be an odd prime, either regular or properly irregular, and let $G$ be a cyclic group of order ${p^2}$. The author determines a full set of inequivalent representations of $G$ by matrices with rational integral entries. This information is used to calculate the ideal class number of the integral group ring $ZG$.References
- Steven Galovich, The class group of a cyclic $p$-group, J. Algebra 30 (1974), 368–387. MR 476838, DOI 10.1016/0021-8693(74)90210-5
- A. Heller and I. Reiner, Representations of cyclic groups in rings of integers. I, Ann. of Math. (2) 76 (1962), 73–92. MR 140575, DOI 10.2307/1970266
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 8-12
- MSC: Primary 20C10; Secondary 12A35
- DOI: https://doi.org/10.1090/S0002-9939-1976-0506781-7
- MathSciNet review: 0506781