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This is a Quantitative Study study.

October 10, 2025Open Access

The permutation dimension of the Klein 4-group

Key Points

The study calculates the p-permutation dimension of the klein 4-group, providing crucial insights into group invariants.
Key measures include indecomposable modules, with specific dimensions computed for each, highlighting their unique characteristics.
Using recent results, the analysis extends understanding of finite p-permutation resolutions relevant to group modules.
Exploring this dimension contributes to broader implications in finite group theory, enriching knowledge on module classifications.

Abstract

Let G be a finite group and k a field of characteristic p > 0. Balmer and Gallauer's recent result on finite p-permutation resolutions of kG-modules motivates the study of an intriguing new invariant; the p-permutation dimension. Following Walsh's success with cyclic groups of prime order, we compute the (global) p-permutation dimension of the Klein 4-group in characteristic p: = 2, along with the dimensions for each of its indecomposable modules.

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Cite This Study

Henry Harman (Tue,) studied this question.

synapsesocial.com/papers/68e861857ef2f04ca37e3982 https://doi.org/https://doi.org/10.48550/arxiv.2507.11469

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