Finiteness of higher \(K\)-groups of orders and group rings
type: Item
instance of: scholarly article
title: Finiteness of higher \(K\)-groups of orders and group rings
zbMATH Open document ID: 1112.19002
author: Aderemi O. Kuku
published in: \(K\)-Theory
publication date: 2007-02-13T00:00:00Z
review text: Let \(R\) be the ring of integers in a number field \(F\) and let \(A\) be an \(R\)-order in a semisimple \(F\)-algebra. It is shown that the groups \(K_{2n}(A)\) and \(G_{2n}(A)\) are finite for all positive integers \(n\). Also, if \(G\) is a finite \(p\)-group, then \(SK_{2n+1}(RG)\) is also a finite \(p\)-group, where \(R\) may now also be a \(p\)-adic ring.
Mathematics Subject Classification ID: 19D50
Mathematics Subject Classification ID: 19D35
Mathematics Subject Classification ID: 19F27
zbMATH DE Number: 5125358
zbMATH Keywords: higher K-group
zbMATH Keywords: transfer map
zbMATH Keywords: order
zbMATH Keywords: division algebras
zbMATH Keywords: group ring
MaRDI profile type: Publication
full work available at URL: s10977-005-3120-8
OpenAlex ID: W2089910913
cites work: Q5562621
cites work: Q3317278
cites work: Q4724810
cites work: K-theory of finite dimensional division algebras
cites work: Some Finiteness Theorems in the K -Theory of Orders in p -Adic Algebras
cites work: Higher algebraic k-theory of group-rings and orders in algebras over number fields
cites work: K-theory of group-rings of finite groups over maximal orders in division algebras
cites work: Some finiteness results in the higher K-theory of orders and group-rings
cites work: Ranks of \(K_n\) and \(G_n\) of orders and group rings of finite groups over integers in number fields
cites work: On the cohomology and K-theory of the general linear groups over a finite field
cites work: Lattices over orders I
cites work: Groupes de Chow et K-théorie de variétés sur un corps fini
DOI: 10.1007/S10977-005-3120-8
description: scientific article; zbMATH DE number 5125358