On simple groups that admit a string C-group representation

Key Points

• 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.