\(SK_1\) of finite abelian groups. II

DOI10.1007/BF01389416zbMath0605.18006OpenAlexW1986941979MaRDI QIDQ1084166

Robert Oliver, Roger C. Alperin, R. Keith Dennis, Michael R. Stein

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143419

zbMATH Keywords

rings of algebraic integersfinite abelian group\(SK_1\)

Mathematics Subject Classification ID

Whitehead groups and (K_1) (19B99) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Grothendieck groups, (K)-theory and commutative rings (13D15) Homological methods in associative algebras (16Exx)

Related Items (9)

Lower bounds for \(K_ 2^{top}({\hat {\mathbb{Z}}}_ p\pi)\) and \(K_ 2({\mathbb{Z}}\pi)\) ⋮ The Whitehead group of (almost) extra-special \(p\)-groups with \(p\) odd ⋮ Constraints on heterotic M-theory from s-cobordism ⋮ On a Note From Oliver Concerning Generalized Euclidean Group Rings ⋮ Nielsen equivalence classes of free Abelianized extensions of groups. ⋮ \(K_ 2\) of p-adic group rings of abelian p-groups ⋮ \(K_2\) of cyclic group rings over \(\lambda\)-rings ⋮ Grothendieck groups of sesquilinear forms over a ring with involution ⋮ Integral group rings: Groups of units and classical K-theory

Cites Work

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• \(SK_1\) of finite Abelian groups. I
• \(SK_1\) for finite groups rings. I
• Induction and structure theorems for orthogonal representations of finite groups
• \(K_2\) of discrete valuation rings
• Grothendieck groups and Picard groups of abelian group rings
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• $SK_1$ for finite group rings: II.
• SK ₁ for Finite Group Rings: IV
• Norms of Units in Group Rings
• Whitehead groups of finite groups
• On explicit reciprocity laws.
• Induction theorems for Grothendieck groups and Whitehead groups of finite groups
• Surjective Stability in Dimension 0 for K 2 and Related Functors

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