Abstract
We prove that a subgroup of the real 3-dimensional special orthogonal group generated by a pair of rotations of respective orders 4 and 8 (belonging to a family of such groups considered by Radin and Sadun in [C. Radin, L. Sadun, On 2-generator subgroups of SO ( 3 ) , Trans. Amer. Math. Soc. 351 (1999) 114469–114480]) has an epimorphic image which is one of PSL ( 2 , p ) , PSL ( 2 , p 2 ) , PGL ( 2 , p ) or PGL ( 2 , p 2 ) (depending on the congruence of p ( mod 16 )) for all odd primes p, by considering its reduction ( mod p ) as a linear group.
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