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A Mayer-Vietoris sequence for class groups. (English) Zbl 0286.12009


MSC:

11R52 Quaternion and other division algebras: arithmetic, zeta functions
16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
11R99 Algebraic number theory: global fields
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References:

[1] Bass, H., Algebraic \(K\)-Theory, (Mathematics Lecture Note Series (1968), Benjamin: Benjamin New York) · Zbl 0248.18025
[2] Bourbaki, N., Algèbre Commutative (1965), Hermann: Hermann Paris, Chapitre 7 · Zbl 0141.03501
[3] Curtis, C. W.; Reiner, I., Representation Theory of Finite Groups and Associative Algebras, (Pure and Applied Mathematics, Vol. XI (1966), Interscience: Interscience New York), MR 26 #2519 · Zbl 1093.20003
[4] Faddeev, D. K., Amer. Math. Soc. Transl., 64, 97-101 (1967), MR 28 #5089 · Zbl 0199.08002
[5] Fröhlich, A., On the classgroup of integral group rings of finite abelian groups, Mathematika, 16, 143-152 (1969), MR 41 #5512 · Zbl 0215.36903
[6] Fröhlich, A., The Picard group of noncommutative rings, in particular of orders, Trans. Amer. Math. Soc., 180, 1-46 (1973) · Zbl 0278.16016
[7] Fröhlich, A., On the classgroup of integral grouprings of finite abelian groups II, Mathematika, 19, 51-56 (1972) · Zbl 0326.20006
[8] Galovich, S.; Reiner, I.; Ullom, S., Class groups for integral representations of metacyclic groups, Mathematika, 19, 105-111 (1972) · Zbl 0248.12010
[9] Hasse, H., Über die Klassenzahl abelscher Zahlkörper (1952), Akademie-Verlag: Akademie-Verlag Berlin · Zbl 0063.01966
[10] Jacobinski, H., Genera and decomposition of lattices over orders, Acta Math., 121, 1-29 (1968) · Zbl 0167.04503
[11] M. A. Kervaire and M. P. Murthy; M. A. Kervaire and M. P. Murthy · Zbl 0355.12009
[12] Lee, M. P., Integral representations of dihedral groups of order \(2p\), Trans. Amer. Math. Soc., 110, 213-231 (1964), MR 28 #139 · Zbl 0126.05403
[13] Martinet, J., Modules sur l’algèbre du groupe quaternionien, Ann. Sci. École Norm. Sup., 4, 399-408 (1971) · Zbl 0219.12012
[14] Milnor, J., Introduction to Algebraic \(K\)-Theory, (Annals of Mathematical Studies No. 72 (1971), Princeton University Press: Princeton University Press Princeton, NJ) · Zbl 0237.18005
[15] Pu, L. C., Integral representations of non-abelian groups of order pq, Michigan Math. J., 12, 231-246 (1965), MR 31 #2321 · Zbl 0136.01701
[16] Reiner, I., Integral representations of cyclic groups of prime order, (Proc. Amer. Math. Soc., 8 (1957)), 142-146, MR 18 #717 · Zbl 0077.25103
[17] Reiner, I., A survey of integral representation theory, Bull. Amer. Math. Soc., 76, 159-227 (1970), MR 40 #7302 · Zbl 0194.04701
[18] Reiner, I.; Ullom, S., Class groups of integral group rings, Trans. Amer. Math. Soc., 170, 1-30 (1972), MR 46 #3605 · Zbl 0253.16023
[19] Swan, R. G., Induced representations and projective modules, Ann. of Math., 71, 552-578 (1960), MR 25 #2131 · Zbl 0104.25102
[20] Swan, R. G., The Grothendieck ring of a finite group, Topology, 2, 85-110 (1963), MR 27 #3683 · Zbl 0119.02905
[21] Swan, R. G.; Evans, E. G., \(K\)-Theory of Finite Groups and Orders, (Lecture Notes No. 149 (1970), Springer-Verlag: Springer-Verlag Berlin/New York)
[22] Takahashi, S., Arithmetic of group representations, Tôhoku Math. J., 11, 216-246 (1959), MR 22 #733 · Zbl 0089.25103
[23] Ullom, S., A note on the classgroup of integral group rings of some cyclic groups, Mathematika, 17, 79-81 (1970), MR 42 #4650 · Zbl 0204.35202
[24] Weiss, E., Algebraic Number Theory (1963), McGraw-Hill: McGraw-Hill New York
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