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The Prime Graph Question for integral group rings asks if it is true that ifthe normalized unit group of the integral group ring of a finite group $G$contains an element of order $pq$, for some primes $p$ and $q$, also $G$contains an element of that order. We answer this question for the three Conwaysporadic simple groups after reducing it to a combinatorial question aboutYoung tableaus and Littlewood-Richardson coefficients. This finishes work of V.Bovdi, A. Konovalov and S. Linton.

On the Prime Graph Question for Integral Group Rings of Conway simple groups