Alternating or Symmetric Groups as Quotients of G~(5,5,60)

摘要

The infinite Coxeter groups G~(k,l,m) are generated by the reflections in the sides of the right hyperbolic triangle forming the fundamental region of the tessellation. Recently, the question when PSL(2, q) or PGL(2, q) is a quotient of G~(m,l,m) has been investigated. An implication of this investigation reveals that, for some special p, PSL(2,p~α) or PGL(2,p~α) is a quotient group of G~(5,5,2τ) which occur as symmetric groups of the map {5,5}_(60). In this paper we show that either A_n or S_n is a quotient of G~(5,5,60) for sufficiently large n.