Primitivity in representations of polycyclic groups

DOI10.1017/S0305004100057327zbMath0438.16005MaRDI QIDQ3879387

Dale L. Harper

Publication date: 1980

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

maximal idealpolycyclic-by-finite grouporbital subgroupirreducible representations of the group algebrasemiprimitive irreducible modulesemiprimitive irreducible representation

Mathematics Subject Classification ID

Group rings (16S34) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (9)

On the primitive representations of finitely generated metabelian groups of finite rank over a field of non-zero characteristic ⋮ On the structure of groups admitting faithful modules with certain conditions of primitivity ⋮ Polycyclic group algebras and theorems of Harper and Lichtman ⋮ Endomorphism rings of simple modules over group rings ⋮ Spectra of conjugated ideals in group algebras of abelian groups of finite rank and control theorems ⋮ The soluble subgroups and the Tits alternative in linear groups over rings of fractions of polycyclic group rings. I ⋮ Arithmeticity of stabilizers of ideals in group rings ⋮ Primitive irreducible representations of finitely generated nilpotent groups ⋮ On the primitive irreducible representations of finitely generated linear groups of finite rank

Cites Work

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• Group rings of polycyclic groups
• Hypercentral ideals, Noetherian modules and a theorem of Stroud
• Representations induced in an invariant subgroup
• On the Finiteness of Certain Soluble Groups
• Primitive Ideals in Group Rings of Polycyclic Groups
• Prime Ideals in Group Rings of Polycyclic Groups

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