Characters vanishing on all but two conjugacy classes

Stephen Michael Gagola, Jr.

Vol. 109 (1983), No. 2, 363–385

DOI: 10.2140/pjm.1983.109.363

Abstract

If the character table of a group G has a row (corresponding to an irreducible character) with precisely two nonzero entries, then G has a unique minimal normal subgroup N which is necessarily an elementary abelian p-group for some prime p. The group G∕O_p(G) is completely determined here. In general, there is no bound on the derived length or nilpotence class of O_p(G).

Mathematical Subject Classification 2000

Primary: 20C15

Milestones

Received: 5 January 1982

Revised: 24 January 1983

Published: 1 December 1983