Permutation dimensions of prime cyclic groups

2025/04/16 by Walsh, Jack · 1 citation
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2504.11841

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by replacing projective resolutions of ring modules with resolutions by p-permutation modules of modules over the group ring. We compute this invariant for cyclic groups of prime order.

Cited by

• The permutation dimension of the Klein 4-group

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• The permutation dimension of the Klein 4-group
• Various Representation Dimensions associated with a Finite Group
• The Benson-Symonds Invariant for Permutation Modules
• Maximal representation dimension of finite p-groups
• Decomposing symmetric powers of certain modular representations of cyclic groups