# Class Groups and Picard Groups of Group Rings and Orders

*Introduction The aim of these lectures is to provide an introduction to recent
developments in the theory of class groups and Picard groups. By way of
orientation, let us indicate where this theory fits into the general framework of
algebra.*

**Author**: Irving Reiner

**Publisher:** American Mathematical Soc.

**ISBN:** 0821816764

**Page:** 44

**View:** 953

# An Introduction to Group Rings

*149] K.W. Roggenkamp and L.L. Scott, Isomorphisms for p-adic group rings, Ann.
Math. 126 (1987), 593-647. 150] K.W. Roggenkamp and M.J. Taylor, Group
Rings and Class Groups, Birkhauser, Basel, Boston and Berlin, 1992. 151] J.*

**Author**: César Polcino Milies

**Publisher:** Springer Science & Business Media

**ISBN:** 9781402002380

**Page:** 371

**View:** 548

# Logarithmic Descriptions of Whitehead Groups and Class Groups for p Groups

*M. Taylor, Locally free classgroups of groups of prime power order, J. Algebra 50
(1978), 463-487. M. Taylor, A logarithmic approach to classgroups of integral
group rings, J. Alg. 66 (1980), 321–353. S. Ullom, The exponent of class groups,
...*

**Author**: Robert Oliver

**Publisher:** American Mathematical Soc.

**ISBN:** 0821824554

**Page:** 97

**View:** 846

# Artinian Modules over Group Rings

*In this book we will consider modules over group rings when the groups have *

certain features, for example, are near to ... In the theory of infinite groups, many

types of groups appear in studying cocentralizers of their conjugacy classes. This

is ...

**Author**: Leonid Kurdachenko

**Publisher:** Springer Science & Business Media

**ISBN:** 3764377658

**Page:** 247

**View:** 471

# Representation Theory of Algebras

*[ 16 ] A Sylowlike theorem for integral group rings of finite solvable groups , Arch .
Math . ... [ 28 ] K. W. Roggenkamp and M. Taylor , Group rings and class groups ,
DMV - Seminar Band 18 , Birkh " a ' auser , Basel Boston Berlin 1992 . ( 29 ) K. W.
...*

**Author**: Raymundo Bautista

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821803950

**Page:** 749

**View:** 439

# Groups Rings and Group Rings

*International Conference : Groups, Rings, and Group Rings, July 28-August 2, *

2008, Ubatuba, Brazil A. Giambruno, César ... Introduction Within the last decade

there has been a growing interest in the class of finitely presented semigroup ...

**Author**: A. Giambruno

**Publisher:** American Mathematical Soc.

**ISBN:** 0821847716

**Page:** 270

**View:** 861

# Groups St Andrews 1981

*K.R. Pearson 8 D.E. Taylor, Groups subnormal in the units of their modular group *

rings, Proc. London Math. Soc. ... I. Reiner G S. Ullom, A Mayer-Victoris sequence

for class groups, J. Algebra 33 (1974), 305-342. P. Ribemboim, Rings and ...

**Author**: C. M. Campbell

**Publisher:** Cambridge University Press

**ISBN:** 0521289742

**Page:** 360

**View:** 827

# Unit Groups of Group Rings

*1965 Some properties of the group ring over rational integers of a finite group ,
Notices Amer Math Soc 12 , 463 . Taussky O ... Ullom S 1970 A note on the class
group of integral group rings of some cyclic groups , Mathematika 17 , 74 - 81 .*

**Author**: Gregory Karpilovsky

**Publisher:** Longman Scientific and Technical

**ISBN:**

**Page:** 393

**View:** 950

# Classgroups of Group Rings

**group rings**. There is an excellent account of the level of knowledge obtained by

such methods in S. Ullom's survey article [U3]. ... motivated by the normal integral

basis problem, introduced a completely new description of such **class**— **groups**.

**Author**: Martin J. Taylor

**Publisher:** Cambridge University Press

**ISBN:** 0521278708

**Page:** 119

**View:** 198

# Abstract Algebra

*Suitable for second to fourth year undergraduates, this title contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of ...*

**Author**: Clive Reis

**Publisher:** World Scientific

**ISBN:** 9814335649

**Page:** 491

**View:** 283

# An Algebraic Introduction to K Theory

*These are groups, rings, or modules whose elements are themselves *

isomorphism classes of groups, rings, ... It focuses on a sequence of abelian

groups Kn(R) associated to each ring ft The first of these is Ko(R), Grothendieck's

group ...

**Author**: Bruce A. Magurn

**Publisher:** Cambridge University Press

**ISBN:** 1107079446

**Page:**

**View:** 583

# Transformation Groups

*T. Petrie J. D. Randall : Transformation Groups on Manifolds , Marcell Dekker
1984 . I. Reiner S. Ullom : Remarks on class groups of integral group rings ,
Symposia Math . vol XIII , 501-516 . R. L. Rubinsztein : On the equivariant
homotopy of ...*

**Author**: Katsuo Kawakubo

**Publisher:** Springer

**ISBN:** 9783540512189

**Page:** 398

**View:** 780

# Introductory Lectures on Rings and Modules

*The main result on finite abelian groups is the structure theorem : every finite
abelian group is isomorphic to a direct sum ... 2.1 Basic definitions and examples
Just as permutation groups form the generic class of groups , endomorphism
rings ...*

**Author**: John A. Beachy

**Publisher:** Cambridge University Press

**ISBN:** 9780521644075

**Page:** 238

**View:** 660

# Group and Semigroup Rings

*Moreover, such group rings are shown to be strongly Lie metabelian and strongly
Lie nilpotent of class at most 3. 1. For any associative ring R we ... groups G
which have a Lie metabelian group ring RG, that is, s!?! (RG) = 0. For a general ...*

**Author**: G. Karpilovsky

**Publisher:** Elsevier

**ISBN:** 9780080872377

**Page:** 266

**View:** 355

# Semisimplicity Conditions for Group Rings of Solvable Groups

*So here one must look for necessary and sufficient conditions on the group which
ces make the group ring semisimple . For the class of abelian groups the group
ring , K [ G ] , is semisimple if and only if G has no elements of Sno order p .*

**Author**: Charles R. Hampton

**Publisher:**

**ISBN:**

**Page:** 70

**View:** 842

# Some Recent Developments in Operator Theory

*W. Gruenberg: Relation modules of finite groups 26. Irving Reiner: Class groups *

and Picord groups of group rings and orders 27. H. Blaine Lawson, Jr.: The

quantitative theory of foliattons 28. T. A. Chapman: Lectures on Hilbert cube

manifolds ...

**Author**: Carl M. Pearcy

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821888810

**Page:** 73

**View:** 822

# Galois Module Structure

*In preparation for the intervention of these analytic invariants in the Hom -
description class - groups , their behaviour under the Galois action of NQ is ... In
Section 2.1 we recall the Hom - description of the class - group of a group - ring .*

**Author**: Victor Percy Snaith

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821871782

**Page:** 207

**View:** 751

# Illinois Journal of Mathematics

# Reviews in Number Theory 1973 83

*... Reiner , Irving ) Class groups for integral representations of metacyclic groups . *

Mathematika 19 ( 1972 ) , 105 - 111 . ( A . Dress ) 48 # 4087 R65 - 211F ( with

Reiner , Irving ) Class groups of integral group rings . Trans . Amer . Math . Soc .

**Author**: Richard K. Guy

**Publisher:**

**ISBN:**

**Page:** 3573

**View:** 509