Let M be a compact n-manifold of positive sectional curvature. We will review classical results on the fundamental group of M, a motivation on the $c\left(n\right)$-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by $c\left(n\right)$, a constant depending only on n, and we will survey partial results (up to date) on the $c\left(n\right)$-cyclic conjecture.