Resumen de Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes

András Pongrácz

• If S is the degree of a permutation group and s is the maximum degree of its elements, then S ≤ 2s − 2. We show that this inequality is sharp for some permutation group if and only if s is a power of 2, and then there is exactly one such permutation group up to isomorphism. The unique example is an elementary Abelian 2-group that arises from a punctured Hadamard code. Then we discuss the solutions of S = 2s − 3 and S = 2s − 4