5.14 (1976)

An intersection of some Sylow 2-subgroups is called a Sylow intersection and an intersection of a pair of Sylow 2-subgroups is called a paired Sylow intersection.
$\qquad$ a) Describe the finite groups all of whose 2-local subgroups have odd indices.
$\qquad$ b) Describe the finite groups all of whose normalizers of Sylow intersections have odd indices.
$\qquad$ c) Describe the finite groups all of whose normalizers of paired Sylow intersections have odd indices.
$\qquad$ d) Describe the finite groups in which for any two Sylow 2-subgroups $P$ and $Q$, the intersection $P \cap Q$ is normal in some Sylow 2-subgroup of $\langle P, Q \rangle$.