Fundamental groups of manifolds of positive sectional curvature

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.