We survey the recent results of the authors on finite groups with a small prime spectrum. The prime spectrum π(G) of a finite group G is the set of prime divisors of its order. If |π(G)|= n then G is called n-primary. We describe the chief factors of 3-primary groups and the chief factors of commutator subgroups of 4-primaxy groups whose prime graphs are disconnected. As a corollary, 3-primary finite almost simple groups and 4-primary finite simple groups recognizable by prime graph are determined. The complete irreducibility of GF(2)A_7-modules in which an element of order 5 acts fixed-point-freely is proved. Finite groups with the same prime graph as the group Aut(J2) or A_(10) are described.
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