Journal of the London Mathematical Society· 2012Q1
Simple groups admit Beauville structures
- 100citations
- Q1SCImago
- 2012year
Short summary
All finite simple groups, except for the alternating group of degree 5, admit unmixed Beauville structures, resolving a conjecture.
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Key points
- Proves that all finite simple groups, except A5, admit unmixed Beauville structures.
- Considers an analog for simple algebraic groups, dependent on character value bounds.
- Demonstrates that any finite simple group contains two conjugacy classes C and D whose elements generate the group when paired.
AI-generated from the title and abstract; the full text is not read.
Abstract
We prove a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit unmixed Beauville structures. We also consider an analog of the result for simple algebraic groups which depends on some upper bounds for character values of regular semisimple elements in finite groups of Lie type. Finally, we prove that any finite simple group contains two conjugacy classes C and D such that any pair of elements in C × D generates the group.
The authors' abstract, as published at the source. Journal of the London Mathematical Society, 2012 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics