Graham Higman posed the question: How small can the integers p and q be made, while maintaining the property that all but finitly many alternating and symmetric groups are factor groups of △(2, p, q)=(x,y: x^2=y^P=(x...Graham Higman posed the question: How small can the integers p and q be made, while maintaining the property that all but finitly many alternating and symmetric groups are factor groups of △(2, p, q)=(x,y: x^2=y^P=(xy)~q=1)? He proved that for a sufficiently large n, the alternating group is a homomorphic image of the triangle group △(2,p, q) where p=3 and q=7. Later, his result was generalized by proving the result for p=3 and q≥7. Choosing p=4 and q≥17 in this paper we have answered the "Hiqman Question".展开更多
文摘Graham Higman posed the question: How small can the integers p and q be made, while maintaining the property that all but finitly many alternating and symmetric groups are factor groups of △(2, p, q)=(x,y: x^2=y^P=(xy)~q=1)? He proved that for a sufficiently large n, the alternating group is a homomorphic image of the triangle group △(2,p, q) where p=3 and q=7. Later, his result was generalized by proving the result for p=3 and q≥7. Choosing p=4 and q≥17 in this paper we have answered the "Hiqman Question".
