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

2017; World Scientific; Volume: 27; Issue: 06 Linguagem: Inglês

10.1142/s0218196717500308

1793-6500

Wolfgang Kimmerle, Alexander Konovalov,

graph theory and CDMA systems

The prime graph question asks whether the Gruenberg–Kegel graph of an integral group ring [Formula: see text], i.e. the prime graph of the normalized unit group of [Formula: see text], coincides with that one of the group [Formula: see text]. In this note, we prove for finite groups [Formula: see text] a reduction of the prime graph question to almost simple groups. We apply this reduction to finite groups [Formula: see text] 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 [Formula: see text].