If you know that G100 must there exist g1 g2 g3 g8 such tha

If you know that |G|=100, must there exist g₁, g₂, g₃, ..., g₈ such that <g₁, g₂, ..., g₈>=100? What if we restrict to just 7 generators? 6 generators?

Solution

If you know that |G|=100, must there exist g1, g2, g3, ..., g8 such that <g1, g2, ..., g8>=100

if we restrict to just 7 generators

<g1, g2, ..., g6.> = 85