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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An explicit formula for the Picard group of the cyclic group of order $p^ 2$
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by Alexander Stolin PDF
Proc. Amer. Math. Soc. 121 (1994), 375-383 Request permission

Abstract:

We give a formula for the Picard group of the integer group ring of the cyclic group of order ${p^2}$ for any odd prime p. As a corollary one gets a formula for properly irregular prime p in terms of Bernoulli numbers.
References
  • Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
  • A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803
  • J. W. S. Cassels and A. Frรถhlich (eds.), Algebraic number theory, Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. MR 0215665
  • Charles W. Curtis and Irving Reiner, Methods of representation theory. Vol. II, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1987. With applications to finite groups and orders; A Wiley-Interscience Publication. MR 892316
  • Steven Galovich, The class group of a cyclic $p$-group, J. Algebra 30 (1974), 368โ€“387. MR 476838, DOI 10.1016/0021-8693(74)90210-5
  • Michel A. Kervaire and M. Pavaman Murthy, On the projective class group of cyclic groups of prime power order, Comment. Math. Helv. 52 (1977), no.ย 3, 415โ€“452. MR 476693, DOI 10.1007/BF02567377
  • John Milnor, Introduction to algebraic $K$-theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. MR 0349811
  • A. Stolin, On the ${K_0}$-group of the integer group ring of the cyclic group of order ${p^2}$, Proceeding of the All-Union Conference on the Theory of Rings, Algebras, Modules, Kishinev, 1980. (Russian) โ€”, On the ${K_0}$-group of the integer group ring of the cyclic group of order ${p^2}$, preprint, Kharkov University, 1980. (Russian) โ€”, On the Picard group of the integer group ring of a cyclic p-group and of rings close to them, preprint, Kharkov Univ., 1984. (Russian)
  • Stephen V. Ullom, Fine structure of class groups of cyclic $p$-groups, J. Algebra 49 (1977), no.ย 1, 112โ€“124. MR 491601, DOI 10.1016/0021-8693(77)90271-X
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 375-383
  • MSC: Primary 11R65; Secondary 11R21, 19A31
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1243832-X
  • MathSciNet review: 1243832