Thompson's conjecture for simple groups with connected prime graph

We deal with finite simple groups G with the property pi(G) aS dagger aEuro parts per thousand{2, 3, 5, 7, 11, 13, 17}, where pi(G) is the set of all prime divisors of the order of a group G. The set of all such groups is denoted by zeta (17). Thompson's conjecture in [1, Question 12.38] is proved valid for all groups in zeta (17) whose prime graph is connected.