On central type factor groups

Shahriar Shahriari

Vol. 151 (1991), No. 1, 151–178

DOI: 10.2140/pjm.1991.151.151

Abstract

Γ is a group of central type if it possesses an irreducible complex character of degree |Γ : Z(Γ)|^1∕2. This is the largest possible degree for an ordinary irreducible character of a finite group. A group G which is isomorphic to Γ∕Z(Γ), where Γ is some group of central type, is called a central type factor group (ctfg). A variety of restrictions on ctfgs are found. These include a local characterization of ctfgs, and restrictions on normal and subnormal structures of ctfgs.

Mathematical Subject Classification 2000

Primary: 20C15

Secondary: 20C25

Milestones

Received: 15 December 1988

Revised: 12 July 1990

Published: 1 November 1991