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arXiv · 1612.05025

On the Gruenberg-Kegel Graph of Integral Group Rings of Finite Groups

Wolfgang Kimmerle·Alexander Konovalov
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Abstract

The prime graph question asks whether the Gruenberg-Kegel graph of an integral group ring $\mathbb Z G$ , i.e. the prime graph of the normalised unit group of $\mathbb Z G$ 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 $G$.

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Wolfgang Kimmerle, Alexander Konovalov. 2016-12-15. On the Gruenberg-Kegel Graph of Integral Group Rings of Finite Groups. https://arxiv.org/abs/1612.05025

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