  Fix a set of primes $\pi$. A finite group is said to satisfy $C_\pi$ or, in
other words, to be a $C_\pi$-group, if it possesses exactly one class of
conjugate $\pi$-Hall subgroups. The pronormality of $\pi$-Hall subgroups in
$C_\pi$-groups is proven, or, equivalently, we prove that $C_\pi$ is inherited
by overgroups of $\pi$-Hall subgroups. Thus an affirmative solution to Problem
17.44(a) from the "Kourovka notebook" is obtained. We also provide an example,
showing that Hall subgroups in finite groups are not pronormal in general.
