[math-fun] Correction re simple group of order 168
In a recent post on the Klein quartic I stated that the simple group of order 168 (call it G) is a subgroup of PSL(2,C) (PSL(2,C) is one way to express the group of all fractional linear transformations over C, aka the group of conformal automorphisms of S^2 =C{^1.) This is incorrect; this group is *not* a subgroup of PSL(2,C). (The finite subgroups of PSL(2,C) are the same as the finite subgroups of SO(3): the cyclic groups C_n, dihedral groups D_n, and rotation groups of the Platonic solids: A_4, S_4,and A_5). G is, however, a subgroup of PSL(3,C) (the group of projective transformations of CP^2, where the Klein quartic naturally lives). (Oddly enough, as I learned from an algebraic geometer friend, the conformal automorphisms of projective varieties in CP^2 of degree <= 4 always extend to CP^2 itself, but this is not necessarily true for degree >= 5.) --Dan
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Daniel Asimov