Extensions and the irreducibilities of induced characters of some 2-groups

Abstract

Let Q n and D n denote the generalized quaternion group and the dihedral group of order 2 n + 1 (n ≥ 2), respectively. Let SD n denote the semidihedral group of order 2 n + 1 (n > 3). Let be a faithful irreducible character of H, where H = Q n or D n or SD n . The purpose of this paper is to determine all 2-groups G such that H C G and the induced character o G is also irreducible.