Class-preserving automorphisms of finite groups with semi-dihedral Sylow 2-subgroups

In this paper, we mainly investigate the class-preserving automorphisms of finite groups whose Sylow subgroups of odd order are all cyclic, with a semi-dihedral Sylow [Formula: see text]-subgroup. We show that finite groups with this property have no non-inner class-preserving automorphisms, which extends some known results. The motivation of our research stems from Burnside’s question and normalizer problem.