An explicit formula for the Picard group of the cyclic group of order
Author:
Alexander Stolin
Journal:
Proc. Amer. Math. Soc. 121 (1994), 375383
MSC:
Primary 11R65; Secondary 11R21, 19A31
MathSciNet review:
1243832
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Abstract: We give a formula for the Picard group of the integer group ring of the cyclic group of order for any odd prime p. As a corollary one gets a formula for properly irregular prime p in terms of Bernoulli numbers.
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, On the group of the integer group ring of the cyclic group of order , preprint, Kharkov University, 1980. (Russian)
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Stephen
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 H. Bass, Algebraic Ktheory, Benjamin, New York, 1968. MR 0249491 (40:2736)
 [BSh]
 Z. I. Borevich and I. R. Shafarevich, Number theory, Academic Press, New York, 1966. MR 0195803 (33:4001)
 [CF]
 J. W. S. Cassels and A. Fröhlich, Algebraic number theory, Thompson Book Co., Washington, DC, 1967. MR 0215665 (35:6500)
 [CR]
 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 pgroup, J. Algebra 30 (1974), 368387. MR 0476838 (57:16390a)
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 M. A. Kervaire and M. P. Murthy, On the projective class group of cyclic groups of prime power order, Comment. Math. Helv. 52 (1977), 415452. MR 0476693 (57:16252)
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 J. Milnor, Introduction to algebraic Ktheory, Ann. of Math. Stud., vol. 72, Princeton Univ. Press, Princeton, NJ, 1971. MR 0349811 (50:2304)
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 A. Stolin, On the group of the integer group ring of the cyclic group of order , Proceeding of the AllUnion Conference on the Theory of Rings, Algebras, Modules, Kishinev, 1980. (Russian)
 [S2]
 , On the group of the integer group ring of the cyclic group of order , preprint, Kharkov University, 1980. (Russian)
 [S3]
 , On the Picard group of the integer group ring of a cyclic pgroup and of rings close to them, preprint, Kharkov Univ., 1984. (Russian)
 [U]
 S. Ullom, Fine structure of class groups of cyclic pgroups, J. Algebra 49 (1977), 112124. MR 0491601 (58:10823)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919941243832X
PII:
S 00029939(1994)1243832X
Article copyright:
© Copyright 1994
American Mathematical Society
