The modular group algebra of a central-elementary-by-abelian p-group

DOI10.1007/BF01197966zbMath0632.16011MaRDI QIDQ1095228

Robert Sandling

Publication date: 1989

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

group of unitsisomorphism problemlower central seriesnormal complementmodular group algebraelementary-abelian-by-abelian p-groups

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15) Units, groups of units (associative rings and algebras) (16U60)

Related Items (14)

Non-isomorphic 2-groups with isomorphic modular group algebras ⋮ Unnamed Item ⋮ A NOTE ON THE DERIVED LENGTH OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA ⋮ Corrigendum to: ``Fuchs' problem for 2-groups ⋮ The modular isomorphism problem: a survey ⋮ Modular group algebras of 2–groups of maximal class ⋮ On circle groups of nilpotent rings of characteristic \(2\) ⋮ The isomorphism problem for group algebras: a criterion ⋮ The modular isomorphism problem and abelian direct factors ⋮ On group invariants determined by modular group algebras: even versus odd characteristic ⋮ A reduction theorem for the isomorphism problem of group algebras over fields ⋮ The modular group algebra problem for metacyclic 𝑝-groups ⋮ The modular isomorphism problem for two generated groups of class two ⋮ On the modular isomorphism problem for groups of class \(3\) and obelisks

Cites Work

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• Units in the modular group algebra of a finite Abelian p-group
• Units in group rings: Splittings and the isomorphism problem
• Units in integral group rings
• Units of integral group rings of metabelian groups
• Normal complements in mod p-envelopes
• Isomorphism of group rings
• Units in metabelian group rings: Non-splitting examples for normalized units
• Group rings of circle and unit groups
• Isomorphism of modular group algebras
• On Automorphisms of Complete Algebras And The Isomorphism Problem for Modular Group Rings
• Groups of Units of Modular Group Algebras
• Presentations for Unit Groups of Modular Group Algebras of Groups of Order 16
• A Note on Normal Complements in mod p Envelopes
• The Modular Group-Ring of a Finite p-Group

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