Magurn, Bruce; Oliver, Robert; Vaserstein, Leonid Units in Whitehead groups of finite groups. (English) Zbl 0517.16011 J. Algebra 84, 324-360 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 Documents MSC: 16S34 Group rings 16U60 Units, groups of units (associative rings and algebras) 16E20 Grothendieck groups, \(K\)-theory, etc. 18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) 11R23 Iwasawa theory Keywords:class number of cyclotomic field; general linear group; subgroup of elementary matrices; order in finite dimensional semisimple algebra; group ring of finite group; totally definite quaternion algebras; Eichler condition; Sylow subgroups; generalised quaternion group; icosahedral group Citations:Zbl 0482.18005 PDFBibTeX XMLCite \textit{B. Magurn} et al., J. Algebra 84, 324--360 (1983; Zbl 0517.16011) Full Text: DOI References: [1] R. C. Alperin, R. K. Dennis, R. Oliver, and M. R. Stein, \( SK_1\) of finite abelian groups, II, to appear.; R. C. Alperin, R. K. Dennis, R. Oliver, and M. R. Stein, \( SK_1\) of finite abelian groups, II, to appear. [2] Bass, H., Algebraic \(K\)-Theory (1968), Benjamin: Benjamin New York · Zbl 0174.30302 [3] Hasse, H., Uber die Klassenzahl abelschen Zahlkorper (1952), Akademie-Verlag: Akademie-Verlag Berlin [4] Higman, G., The units of group rings, (Proc. London Math. Soc., 46 (1940)), 231-248, (2) · JFM 66.0104.04 [5] Jajodia, S.; Magurn, B. A., Surjective stability of units and simple homotopy type, J. Pure Appl. Algebra, 18, 45-58 (1980) · Zbl 0438.57008 [6] Keating, M. E., On the \(K\)-theory of the quaternion group, Mathematika, 20, 59-62 (1973) · Zbl 0267.18016 [7] Koblitz, N., \(p\)-adic Numbers, \(p\)-adic Analysis, and Zeta-Functions, (GTM 58 (1977), Springer-Verlag: Springer-Verlag New York/Berlin) · Zbl 0364.12015 [8] Lang, S., Algebraic Number Theory (1970), Addison-Wesley: Addison-Wesley Reading, Mass. · Zbl 0211.38404 [9] Magurn, B. A., \( SK_1\) of dihedral groups, J. Algebra, 51, 2, 399-415 (1978) · Zbl 0376.16026 [10] Magurn, B. A., Images of \(SK_1 ZG \), Pacific J. Math., 79, 2, 531-539 (1978) · Zbl 0398.16007 [11] Oliver, R., Invent. Math., 64, 167-169 (1981), See correction in · Zbl 0455.18007 [12] Oliver, R., \( SK_1\) for finite group rings, II, Math. Scand., 47, 195-231 (1980) · Zbl 0456.16027 [13] Oliver, R., \( SK_1\) for finite group rings, III, (Algebraic \(K\)-Theory (Evanston 1980). Algebraic \(K\)-Theory (Evanston 1980), Lecture Notes in Mathematics No. 854 (1981), Springer-Verlag: Springer-Verlag New York/Berlin), 299-337 [14] Oliver, R., \( SK_1\) for finite group rings, IV, (Proc. London Math. Soc., 46 (1983)), 1-37, (3) · Zbl 0499.16017 [15] Reiner, I., Maximal Orders (1975), Academic Press: Academic Press London/New York · Zbl 0305.16001 [16] Swan, R. G., Strong approximation and locally free modules, (Ring Theory and Algebra III, Proceedings of the Third Oklahoma Conference (1980), Dekker: Dekker New York), 153-223 [17] Vaserstein, L. N., Math. USSR Sb., 8, No. 3, 383-400 (1969) · Zbl 0238.20057 [18] Vaserstein, L. N., The structure of classical arithmetic groups of rank greater than one, Math. USSR Sb., 20, 465-491 (1973) · Zbl 0291.14016 [19] Vaserstein, L. N., Stable rank of rings and dimensionality of topological spaces, Funct. Anal. Appl., 5, 102-110 (1971) · Zbl 0239.16028 [20] Wall, C. T.C, On the classification of hermitian forms: III: Complete semilocal rings, Invent. Math., 19, 59-71 (1973) · Zbl 0259.16013 [21] Wall, C. T.C, Norms of units in group rings, (Proc. London Math. Soc., 29 (1974)), 593-632, (3) · Zbl 0302.16013 [22] Weil, A., Basic Number Theory, (Die Grundlehren der math. Wissenschaften, 144 (1967), Springer-Verlag: Springer-Verlag New York/Berlin) · Zbl 0823.11001 [23] Weiss, E., Algebraic Number Theory (1963), Chelsea: Chelsea New York [24] Williamson, S., Crossed products and hereditary orders, Nagoya Math. J., 23, 103-120 (1963) · Zbl 0152.02002 [25] Wilson, S. M.J, Reduced norms in the \(K\)-theory of orders, J. Algebra, 46, 1-11 (1977) · Zbl 0358.16021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.