A subgroup of SO(3, R) generated by rotations of orders 4 and 8

[摘要] 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. Raclin, L. Sadun, On 2-generator subgroups of SO(3), Trans. Amer. Math. Soc. 351 (1999) 114469114480]) 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. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01