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Abstract
The prime graph question asks whether the Gruenberg–Kegel graph of an integral group ring ℤG, i.e. the prime graph of the normalized unit group of ℤG, coincides with that one of the group G. In this note, we prove for finite groups G a reduction of the prime graph question to almost simple groups. We apply this reduction to finite groups G whose order is divisible by at most three primes and show that the Gruenberg–Kegel graph of such groups coincides with the prime graph of G.
Original language  English 

Pages (fromto)  619631 
Number of pages  13 
Journal  International Journal of Algebra and Computation 
Volume  27 
Issue number  06 
DOIs  
Publication status  Published  24 Aug 2017 
Keywords
 Integral group rings
 Torsion units
 Gruenberg–Kegel graph
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Dive into the research topics of 'On the Gruenberg–Kegel graph of integral group rings of finite groups'. Together they form a unique fingerprint.Projects
 1 Finished

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)
1/03/15 → 29/02/20
Project: Standard
Profiles

Olexandr Konovalov
 School of Computer Science  Lecturer
 Institute of Behavioural and Neural Sciences
 Centre for Interdisciplinary Research in Computational Algebra
 St Andrews GAP Centre
Person: Academic, Academic  Research