Applications of dimension subgroups to the power structure of \(p\)-groups

DOI10.1007/BF02773423zbMath0734.20008MaRDI QIDQ810630

Aner Shalev, Carlo Maria Scoppola

Publication date: 1991

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

classfinite \(p\)-groupspower structuredimension subgroupsproducts of \(p^{i+k}th\) powers

Mathematics Subject Classification ID

Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Torsion elements in \(p\)-adic analytic pro-\(p\) groups. ⋮ Dimension subgroups and \(p\)-th powers in \(p\)-groups.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Powerful \(p\)-groups. I: Finite groups.
• Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras
• The power structure of \(p\)-groups. I
• Group rings and their augmentation ideals
• The power-commutator structure of finite p-groups
• Isomorphism of modular group algebras
• Note on a basis of P. Hall for the higher commutators in free groups
• Unipotent Representations of Nilpotent Groups
• LOEWY STRUCTURE OF PERMUTATION MODULES FOR p-GROUPS
• Lie Dimension Subgroups, Lie Nilpotency Indices, and the Exponent of the Group of Normalized Units
• Groups of Prime Power Order as Frobenius-Wielandt Complements
• Lie dimension subgroups
• The class of a nilpotent wreath product
• A Contribution to the Theory of Groups of Prime-Power Order
• Endliche Gruppen I
• The Structure of the Group Ring of a p-Group Over a Modular Field
• Sur les groupes nilpotents et les anneaux de Lie