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

Geoffrey Raymond Robinson

doi:10.1016/j.jalgebra.2006.04.034

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

Geoffrey Raymond Robinson

Mathematical Science

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2 Citations (Scopus)

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. 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.

Original language	English
Pages (from-to)	201-207
Number of pages	7
Journal	Journal of Algebra
Volume	306
Issue number	1
Early online date	30 May 2006
DOIs	https://doi.org/10.1016/j.jalgebra.2006.04.034
Publication status	Published - 1 Dec 2006

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10.1016/j.jalgebra.2006.04.034

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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. 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.",

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AB - 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.

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

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