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Why is \(\mathrm{PSL}(2,7)\cong\mathrm{GL}(3,2)\)? (English) Zbl 1229.20046
Summary: We construct a straightforward, explicit isomorphism from the group \(\mathrm{PSL}(2,7)\) onto the group \(\mathrm{GL}(3,2)\). Our proof requires only elementary facts about groups, fields, and matrices. In particular, our proof does not utilize projective geometry, block designs, or simplicity arguments.

MSC:
20G40 Linear algebraic groups over finite fields
20D06 Simple groups: alternating groups and groups of Lie type
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