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

2016/12/15 by Wolfgang Kimmerle, Kimmerle, Wolfgang, Olexandr Konovalov +1 · 2 citations
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1612.05025

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.

Cited by

• The N-prime graph and the Subgroup Isomorphism Problem
• The N-Prime Graph Question is equivalent to the Prime Graph Question

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