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Class groups of cyclic p-groups

Published online by Cambridge University Press:  26 February 2010

Robert Oliver
Robert Oliver
Affiliation:
Matematisk Institut, Ny Munkegade-Byning 530, 8000 Aarhus C, Denmark
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Extract

As usual, if π is a finite group and ℳ ⊆ ℚπ a maximal order containing , we set

This is well known to be a finite group, and independent of the choice of ℳ.

Type
Research Article
Information
Mathematika , Volume 30 , Issue 1 , June 1983 , pp. 26 - 57
Copyright
Copyright © University College London 1983

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References

1.Fröhlich, A.. On the class group of integral group rings of finite Abelian groups II. Mathematika, 19 (1972), 51–56.CrossRefGoogle Scholar
2. Fröhlich, A.. Locally free modules over arithmetic orders. J. reine und angew. Math., 274/275 (1975), 112–124.Google Scholar
3.Galovich, S.. The class group of a cyclic p-group. J. Algebra, 30 (1974), 368–387.CrossRefGoogle Scholar
4.Galovich, S.. Corrigendum: The class group of a cyclic p-group. J. Algebra, 47 (1977), 547–548.CrossRefGoogle Scholar
5.Hambleton, I. and Milgram, R. J.. The surgery obstruction groups for finite 2-groups. Invent. Math., 61 (1980), 33–52.CrossRefGoogle Scholar
6.Kervaire, M. and Murthy, M. P.. On the projective class group of cyclic groups of prime power order. Comment. Math. Helv., 52 (1977), 415–452.CrossRefGoogle Scholar
7.Lang, S.. Cyclotomic fields (Springer-Verlag, 1978).CrossRefGoogle Scholar
8.Oliver, R.. SK, for finite group rings: II. Math. Scand., 47 (1980), 195–231.CrossRefGoogle Scholar
9.Ullom, S.. Fine structure of class groups of cyclic p-groups. J. Algebra, 49 (1977), 112–124.CrossRefGoogle Scholar
10.Ullom, S.. Class groups of cyclotomic fields and group rings. J. London Math. Soc, 17 (1978), 231–239.CrossRefGoogle Scholar