Recent advances on torsion subgroups of integral group rings

Wolfgang Kimmerle; Alexander Konovalov

doi:10.1017/CBO9781316227343.021

Recent advances on torsion subgroups of integral group rings

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

This survey reports on recent progress made on finite subgroups of the unit group of integral group rings of finite groups. We show that the Gruenberg–Kegel graph of ZG coincides with that one of G provided |G| is divisible by at most three primes and give an outline how such a result may be obtained with the aid of computational algebra. In the last section we discuss this question for sporadic simple groups and their automorphism groups.

Original language	English
Title of host publication	Groups St Andrews 2013
Place of Publication	Cambridge
Publisher	Cambridge University Press
Pages	331-347
Number of pages	17
ISBN (Electronic)	9781316468913
ISBN (Print)	9781107514546
DOIs	https://doi.org/10.1017/CBO9781316227343.021
Publication status	Published - 2015

Publication series

Name	London Mathematical Society Lecture Note Series

Access to Document

10.1017/CBO9781316227343.021

Cite this

@inbook{047241885f574cb59fd9b9b43a0570ac,

title = "Recent advances on torsion subgroups of integral group rings",

abstract = "This survey reports on recent progress made on finite subgroups of the unit group of integral group rings of finite groups. We show that the Gruenberg–Kegel graph of ZG coincides with that one of G provided |G| is divisible by at most three primes and give an outline how such a result may be obtained with the aid of computational algebra. In the last section we discuss this question for sporadic simple groups and their automorphism groups.",

author = "Wolfgang Kimmerle and Alexander Konovalov",

year = "2015",

doi = "10.1017/CBO9781316227343.021",

language = "English",

isbn = "9781107514546",

series = "London Mathematical Society Lecture Note Series",

publisher = "Cambridge University Press",

pages = "331--347",

booktitle = "Groups St Andrews 2013",

address = "United Kingdom",

}

TY - CHAP

T1 - Recent advances on torsion subgroups of integral group rings

AU - Kimmerle, Wolfgang

AU - Konovalov, Alexander

PY - 2015

Y1 - 2015

N2 - This survey reports on recent progress made on finite subgroups of the unit group of integral group rings of finite groups. We show that the Gruenberg–Kegel graph of ZG coincides with that one of G provided |G| is divisible by at most three primes and give an outline how such a result may be obtained with the aid of computational algebra. In the last section we discuss this question for sporadic simple groups and their automorphism groups.

AB - This survey reports on recent progress made on finite subgroups of the unit group of integral group rings of finite groups. We show that the Gruenberg–Kegel graph of ZG coincides with that one of G provided |G| is divisible by at most three primes and give an outline how such a result may be obtained with the aid of computational algebra. In the last section we discuss this question for sporadic simple groups and their automorphism groups.

UR - https://www.cambridge.org/gb/academic/subjects/mathematics/algebra/groups-st-andrews-2013?format=PB

U2 - 10.1017/CBO9781316227343.021

DO - 10.1017/CBO9781316227343.021

M3 - Chapter

AN - SCOPUS:84954137416

SN - 9781107514546

T3 - London Mathematical Society Lecture Note Series

SP - 331

EP - 347

BT - Groups St Andrews 2013

PB - Cambridge University Press

CY - Cambridge

ER -

Recent advances on torsion subgroups of integral group rings

Abstract

Publication series

Access to Document

Other files and links

Fingerprint

HPC-GAP: High performance computational: HPC-GAP High Performance Computational Algebra and Discrete Mathematics

Olexandr Konovalov

Cite this

Recent advances on torsion subgroups of integral group rings

Abstract

Publication series

Access to Document

Other files and links

Fingerprint

Projects

HPC-GAP: High performance computational: HPC-GAP High Performance Computational Algebra and Discrete Mathematics

Profiles

Olexandr Konovalov

Cite this