Let G be a finite group. The prime graph of G is a graph Γ(G) with vertex set π(G) and the set of all prime divisors of |G|, where two distinct vertices p and q are joined by an edge if G has an element of order pq. We prove that if Γ(G) = Γ(G2(5)), then G has a normal subgroup N such that π(N) ⊆ {2, 3, 5} and G/N ≅ G 2(5).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 8, pp. 1142–1146, August, 2016.
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Nosratpour, P., Darafsheh, M.R. Characterization of the Group G 2(5) by the Prime Graph. Ukr Math J 68, 1308–1313 (2017). https://doi.org/10.1007/s11253-017-1296-8
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DOI: https://doi.org/10.1007/s11253-017-1296-8