On the Gruenberg–Kegel graph of integral group rings of finite groups
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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.
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
International Journal of Algebra and Computation
© 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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