August 26, 2025The Art of Discrete and Applied MathematicsOpen Access

On simple groups that admit a string C-group representation

View Full Paper

Ask AI

Bookmark

A simple group has a C-group representation unless it is among PSL(3, q) or other noted groups, showing clear limits.
Key exceptions include PSL(4, 2n), PSU(4, 3), A₆, and other names, which do not meet the criteria for representation.
The result was achieved by proving a necessary and sufficient condition for such group representations to exist.
This finding enhances the understanding of group theory and the limits of representations for certain simple groups.

Implication

This proves that simple groups may possess C-group representations, highlighting exceptions among notable groups.

Abstract

We prove that a simple group admits at least one string C-group representation if and only if it is not one of PSL(3, q), PSU(3, q), PSL(4, 2n), PSU(4, 2n), PSU(4, 3), PSU(5, 2), A₆, A₇, M₁₁, M₂₂, M₂₃ or McL.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Leemans et al. (2025) studied this question.

synapsesocial.com/papers/68af63e9ad7bf08b1eae45fa https://doi.org/10.26493/2590-9770.1329.6f5

View Full Paper

Ask AI

Bookmark

Implication

This proves that simple groups may possess C-group representations, highlighting exceptions among notable groups.

On simple groups that admit a string C-group representation

Key Points

Implication

Abstract

Discussion

Cite This Study

On simple groups that admit a string C-group representation

Key Points

Implication

Abstract

Discussion

Cite This Study