Characteristic ideals in group algebras

Indranand Sinha

Vol. 55 (1974), No. 1, 285–287

DOI: 10.2140/pjm.1974.55.285

Abstract

If FG is the group-algebra of a group G over a field F, and U is any subgroup of the automorphism group of the F-algebra FG, then an ideal I of FG, is called A-characteristic if I^α ⊆ I,∀^α ∈ A. If A is the whole automorphism group itself, then we merely say that I is characteristic. Then D.S. Passman has proved the following result: “Let H⊲G such that G∕H is F-complete. Then for each characteristic ideal I of FG,I = (I ∩FH)FG.” The main concern in this paper is to consider the converse of this result.

Mathematical Subject Classification

Primary: 16A26

Milestones

Received: 18 April 1973

Published: 1 November 1974