Infinite groups admitting a faithful irreducible representation

Abstract

Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated. We consider locally finite groups and groups whose socle is essential.2010 Mathematics Subject Classification. 20C07.

Primitive irreducible representations of finitely generated nilpotent groups

“…There are many results which show that the existence of a faithful irreducible representation of a group G over a field F may have essential influence on the structure of the group G (see for instance [11][12][13][14][15][16][17]). Certainly, primitive irreducible modules are a basic subject for investigations when we are dealing with irreducible representations.…”

On the Primitive Irreducible Representations of Finitely Generated Linear Groups of Finite Rank

“…Naturally, the following question appears: what can be said on the construction of a group G if it has a faithful primitive irreducible representation over a field k? It should be noted that there are many results which show that the existence of a faithful irreducible representation of a group G over a field k may have essential influence on the structure of the group G (see for instance [11][12][13][14][18][19][20]).…”