Transitive groups of degree 2p + k

Abstract.

Let p be an odd prime. We study transitive groups of degree n = 2p + k where k is 1, 2 or p. A transitive group G (|G| even) of degree 2p + 1 is doubly transitive of degree 2p + 1 if and only if G admits an element of order p degree 2p. A primitive group G (|G _a | even) of degree 2p + 2 is triply transitive of degree 2p + 2 if and only if G admits an element of order p degree 2p. A primitive group G (|G| even) of degree 3p with rank less than 4 is doubly transitive if p is not of the form 3a ² + 3a + 1 or (3b ² + 3b + 2 ) /4.