scholarly journals Higher K -theory of group-rings of virtually infinite cyclic groups

2003 ◽  
Vol 325 (4) ◽  
pp. 711-726 ◽  
Author(s):  
Aderemi O. Kuku ◽  
Guoping Tang
Keyword(s):  
Group Rings ◽  
Cyclic Groups ◽  
K Theory

A Universal Coefficient Decomposition for Subgroups Induced by Submodules of Group Algebras

1997 ◽  
Vol 40 (1) ◽  
pp. 47-53 ◽  
Author(s):  
Manfred Hartl
Keyword(s):  
Group Algebra ◽  
Prime Power ◽  
Decomposition Theorem ◽  
Group Algebras ◽  
Group Rings ◽  
Prime Power Order ◽  
Relative Dimension ◽  
Theoretical Methods ◽  
Cyclic Groups ◽  
Coefficient Ring

AbstractDimension subgroups and Lie dimension subgroups are known to satisfy a ‘universal coefficient decomposition’, i.e. their value with respect to an arbitrary coefficient ring can be described in terms of their values with respect to the ‘universal’ coefficient rings given by the cyclic groups of infinite and prime power order. Here this fact is generalized to much more general types of induced subgroups, notably covering Fox subgroups and relative dimension subgroups with respect to group algebra filtrations induced by arbitrary N-series, as well as certain common generalisations of these which occur in the study of the former. This result relies on an extension of the principal universal coefficient decomposition theorem on polynomial ideals (due to Passi, Parmenter and Seghal), to all additive subgroups of group rings. This is possible by using homological instead of ring theoretical methods.

scholarly journals Calculation of Two-Primary Algebraic K -Theory of Some Group Rings

K-Theory ◽  
1999 ◽  
Vol 16 (4) ◽  
pp. 391-397 ◽  
Author(s):  
Paul arne østvær
Keyword(s):  
Group Rings ◽  
K Theory

scholarly journals Algebraic K-theory of group rings and the cyclotomic trace map

2017 ◽  
Vol 304 ◽  
pp. 930-1020 ◽  
Author(s):  
Wolfgang Lück ◽  
Holger Reich ◽  
John Rognes ◽  
Marco Varisco
Keyword(s):  
Group Rings ◽  
Trace Map ◽  
K Theory

Units in Group Rings of Free Products of Prime Cyclic Groups

1998 ◽  
Vol 50 (2) ◽  
pp. 312-322 ◽  
Author(s):  
Michael A. Dokuchaev ◽  
Maria Lucia Sobral Singer
Keyword(s):  
Unit Group ◽  
Group Rings ◽  
Rational Group ◽  
Free Products ◽  
Structural Result ◽  
Cyclic Groups ◽  
Amalgamated Free Products ◽  
Products Of Groups ◽  
Finite Subgroups ◽  
Zassenhaus Conjecture

AbstractLet G be a free product of cyclic groups of prime order. The structure of the unit group U(ℚG) of the rational group ring ℚG is given in terms of free products and amalgamated free products of groups. As an application, all finite subgroups of U(ℚG), up to conjugacy, are described and the Zassenhaus Conjecture for finite subgroups in ℤ G is proved. A strong version of the Tits Alternative for U(ℚG) is obtained as a corollary of the structural result.

K -Theory for Twisted Group Rings

1974 ◽  
Vol s3-29 (2) ◽  
pp. 257-271 ◽  
Author(s):  
S. M. J. Wilson
Keyword(s):  
Group Rings ◽  
Twisted Group ◽  
K Theory

scholarly journals SL2 over group rings of cyclic groups

1990 ◽  
Vol 134 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Said Sidki
Keyword(s):  
Group Rings ◽  
Cyclic Groups
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