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On the Gruenberg–Kegel graph of integral group rings of finite groups

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Date
24/08/2017
Author
Kimmerle, Wolfgang
Konovalov, Alexander
Funder
EPSRC
Grant ID
EP/M022641/1
Keywords
Integral group rings
Torsion units
Gruenberg–Kegel graph
QA75 Electronic computers. Computer science
T-NDAS
BDC
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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.
Citation
Kimmerle , W & Konovalov , A 2017 , ' On the Gruenberg–Kegel graph of integral group rings of finite groups ' , International Journal of Algebra and Computation , vol. 27 , no. 06 , pp. 619-631 . https://doi.org/10.1142/S0218196717500308
Publication
International Journal of Algebra and Computation
Status
Peer reviewed
DOI
https://doi.org/10.1142/S0218196717500308
ISSN
0218-1967
Type
Journal article
Rights
© 2017, World Scientific Publishing Company. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.worldscientific.com / https://doi.org/10.1142/S0218196717500308
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/15872

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