Integral representations: Genus, k-theory and class groups

1978 ◽  
pp. 52-69 ◽  
Author(s):  
Irving Reiner
Keyword(s):  
Integral Representations ◽  
Class Groups ◽  
K Theory

scholarly journals Algebraic K-Theory of Mapping Class Groups

K-Theory ◽  
2004 ◽  
Vol 32 (1) ◽  
pp. 83-100 ◽  
Author(s):  
Ethan Berkove ◽  
Daniel Juan-Pineda ◽  
Qin Lu
Keyword(s):  
Mapping Class Groups ◽  
Mapping Class ◽  
Class Groups ◽  
K Theory

Higher Class Groups of Locally Triangular Orders over Number Fields

2009 ◽  
Vol 16 (01) ◽  
pp. 79-84 ◽  
Author(s):  
Xuejun Guo ◽  
Aderemi Kuku
Keyword(s):  
Class Group ◽  
Number Fields ◽  
Prime Ideals ◽  
Class Groups ◽  
K Theory

In this paper, we study the K-theory of triangular rings. As an application, we show that for a locally triangular order Λ, the p-torsion in the higher class group Cl2n(Λ) can only occur for primes p which lie under the prime ideals ℘ of [Formula: see text], at which Λ is not maximal.

Class groups for integral representations of metacyclic groups

Mathematika ◽  
1972 ◽  
Vol 19 (1) ◽  
pp. 105-111 ◽  
Author(s):  
S. Galovich ◽  
I. Reiner ◽  
S. Ullom
Keyword(s):  
Integral Representations ◽  
Class Groups ◽  
Metacyclic Groups

K-theory of mapping class groups: generalp-adicK-theory for punctured spheres

1995 ◽  
Vol 218 (1) ◽  
pp. 611-634 ◽  
Author(s):  
Luke Hodgkin
Keyword(s):  
Mapping Class Groups ◽  
Mapping Class ◽  
Class Groups ◽  
K Theory

scholarly journals $K$-theory and right ideal class groups for HNP rings

1987 ◽  
Vol 302 (2) ◽  
pp. 751-751
Author(s):  
Timothy J. Hodges
Keyword(s):  
Ideal Class ◽  
Class Groups ◽  
Ideal Class Groups ◽  
K Theory

Integral representations ofp-class groups in ? p -extensions, semisimple differentials and jacobians

1991 ◽  
Vol 56 (3) ◽  
pp. 254-269 ◽  
Author(s):  
Gabriel D. Villa Salvador ◽  
Manohar L. Madan
Keyword(s):  
Integral Representations ◽  
Class Groups

The Discrete Logarithm in Logarithmic l-Class Groups and Its Applications in K-theory

2004 ◽  
pp. 367-378
Author(s):  
Sebastian Pauli ◽  
Florence Soriano-Gafiuk
Keyword(s):  
Discrete Logarithm ◽  
Class Groups ◽  
K Theory

scholarly journals An extension theorem for integral representations

1997 ◽  
Vol 63 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Wolfgang Knapp ◽  
Peter Schmid
Keyword(s):  
Finite Group ◽  
Matrix Representation ◽  
Extension Theorem ◽  
Iwasawa Theory ◽  
Integral Representations ◽  
Roots Of Unity ◽  
Cyclotomic Fields ◽  
Qualitative Result ◽  
Class Groups ◽  
A Finite Group

AbstractBy a fundamental theorem of Brauer every irreducible character of a finite group G can be written in the field Q(εm) of mth roots of unity where m is the exponent of G. Is it always possible to find a matrix representation over its ring Z[εm] of integers? In the present paper it is shown that this holds true provided it is valid for the quasisimple groups. The reduction to such groups relies on a useful extension theorem for integral representations. Iwasawa theory on class groups of cyclotomic fields gives evidence that the answer is at least affirmative when the exponent is replaced by the order, and provides for a general qualitative result.

K-Theory and Right Ideal Class Groups for HNP Rings

1987 ◽  
Vol 302 (2) ◽  
pp. 751 ◽  
Author(s):  
Timothy J. Hodges
Keyword(s):  
Ideal Class ◽  
Class Groups ◽  
Ideal Class Groups ◽  
K Theory

On the K -Theory of Small Mapping Class Groups

1994 ◽  
Vol 49 (3) ◽  
pp. 594-613
Author(s):  
Luke Hodgkin
Keyword(s):  
Mapping Class Groups ◽  
Mapping Class ◽  
Class Groups ◽  
K Theory
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