Rational Conjugacy of Torsion Units in Integral Group Rings of Non-Solvable Groups-Reference-Cited by-同舟云学术

Rational Conjugacy of Torsion Units in Integral Group Rings of Non-Solvable Groups

Published:2017-03-16 Issue:4 Volume:60 Page:813-830
ISSN:0013-0915
Container-title:Proceedings of the Edinburgh Mathematical Society
language:en
Short-container-title:Proceedings of the Edinburgh Mathematical Society

Author:

Bächle Andreas,Margolis Leo

Abstract

AbstractWe introduce a new method to study rational conjugacy of torsion units in integral group rings using integral and modular representation theory. Employing this new method, we verify the first Zassenhaus conjecture for the group PSL(2, 19). We also prove the Zassenhaus conjecture for PSL(2, 23). In a second application we show that there are no normalized units of order 6 in the integral group rings of M10 and PGL(2, 9). This completes the proof of a theorem of Kimmerle and Konovalov that shows that the prime graph question has an affirmative answer for all groups having an order divisible by at most three different primes.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference34 articles.

1. Representations of finite groups over number rings;Gudivok;Izv. Akad. Nauk SSSR Ser. Mat.,1967

2. Wilson R. , Walsh P. , Tripp J. , Suleiman I. , Parker R. , Norton S. , Nickerson S. , Linton S. , Bray J. and Abbott R. , Atlas of finite group representations, Version 3 (available at http://brauer.maths.qmul.ac.uk/Atlas/v3/; 2014).

3. Dabbaghian V. , REPSN – a GAP4 package for constructing representations of finite groups, Version 3.0.2, GAP package (available at http://www.sfu.ca/~vdabbagh/gap/repsn.html; 2011).

4. Zassenhaus conjecture forA 5

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