Brown, Ezra; Loehr, Nicholas Why is \(\mathrm{PSL}(2,7)\cong\mathrm{GL}(3,2)\)? (English) Zbl 1229.20046 Am. Math. Mon. 116, No. 8, 727-732 (2009). 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. Cited in 1 ReviewCited in 6 Documents MSC: 20G40 Linear algebraic groups over finite fields 20D06 Simple groups: alternating groups and groups of Lie type Keywords:explicit isomorphisms; \(\mathrm{PSL}(2,7)\); \(\mathrm{GL}(3,2)\) PDFBibTeX XMLCite \textit{E. Brown} and \textit{N. Loehr}, Am. Math. Mon. 116, No. 8, 727--732 (2009; Zbl 1229.20046) Full Text: DOI