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

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 $G$.

arXiv comment9 pages

References in corpus (2)

• Reliability and reproducibility of Atlas information
• Constructing the ordinary character tables of some Atlas groups using character theoretic methods