Journal of Algebra and Its Applications· 2026Q2
Representation Dimension of Some Finite Groups
- 0citations
- Q2SCImago
- 2026year
Short summary
The representation dimension of finite groups is computed for p-groups up to order p^5, their direct products, and groups with specific nonlinear character conditions, establishing the minimal degree of a complex faithful representation.
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Key points
- Computes the representation dimension for finite p-groups up to order p^5.
- Calculates representation dimension for direct products of these p-groups.
- Determines representation dimension for groups with specific nonlinear irreducible character conditions.
- Identifies the minimal degree of a complex faithful irreducible representation for these groups.
AI-generated from the title and abstract; the full text is not read.
Abstract
For a finite group G, the representation dimension is the minimal degree of a complex faithful representation of G. In this article, we compute representation dimension for some finite p-groups, in particular, for all p-groups of order up to p 5 , their direct products, and groups with certain conditions on nonlinear irreducible characters. We also compute the minimal degree of a complex faithful irreducible representation of such groups, if one exists. In the appendix, we present GAP codes to compute these numbers.
The authors' abstract, as published at the source. Journal of Algebra and Its Applications, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics