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Integral representations of cyclic groups of order $ p\sp{2}$


Author: Irving Reiner
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
Erratum: Proc. Amer. Math. Soc. 63 (1977), 374.
MathSciNet review: 0506781
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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 [Enhancements On Off] (What's this?)

  • [1] S. Galovich, The class group of a cyclic $ p$-group, J. Algebra 30 (1974), 368-387. MR 0476838 (57:16390a)
  • [2] A. Heller and I. Reiner, Representations of cyclic groups in rings of integers. I, Ann. of Math. (2) 76 (1962), 73-92. MR 25 #3993. MR 0140575 (25:3993)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0506781-7
Article copyright: © Copyright 1976 American Mathematical Society

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