Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

An explicit formula for the Picard group of the cyclic group of order $ p\sp 2$


Author: Alexander Stolin
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [B] H. Bass, Algebraic K-theory, Benjamin, New York, 1968. MR 0249491 (40:2736)
  • [B-Sh] Z. I. Borevich and I. R. Shafarevich, Number theory, Academic Press, New York, 1966. MR 0195803 (33:4001)
  • [C-F] J. W. S. Cassels and A. Fröhlich, Algebraic number theory, Thompson Book Co., Washington, DC, 1967. MR 0215665 (35:6500)
  • [C-R] C. W. Curtis and I. Reiner, Methods of representation theory, vol. II, Wiley, New York, 1987. MR 892316 (88f:20002)
  • [G] S. Galovich, The class group of a cyclic p-group, J. Algebra 30 (1974), 368-387. MR 0476838 (57:16390a)
  • [K-M] M. A. Kervaire and M. P. Murthy, On the projective class group of cyclic groups of prime power order, Comment. Math. Helv. 52 (1977), 415-452. MR 0476693 (57:16252)
  • [M] J. Milnor, Introduction to algebraic K-theory, Ann. of Math. Stud., vol. 72, Princeton Univ. Press, Princeton, NJ, 1971. MR 0349811 (50:2304)
  • [S1] 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)
  • [S2] -, On the $ {K_0}$-group of the integer group ring of the cyclic group of order $ {p^2}$, preprint, Kharkov University, 1980. (Russian)
  • [S3] -, 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)
  • [U] S. Ullom, Fine structure of class groups of cyclic p-groups, J. Algebra 49 (1977), 112-124. MR 0491601 (58:10823)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11R65, 11R21, 19A31

Retrieve articles in all journals with MSC: 11R65, 11R21, 19A31


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1243832-X
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society