We begin with a simple observation as to when an abstract central extension of a compact p-adic analytic group by a finite group is topological. Following that, we consider G = G(k) where G is a semi-simple algebraic group over a non-archimedean local field k such that k-rank(G) ≥ 4, and A is a finite abelian p-group where p is the residue characteristic of k. We use the Tits building to prove that H2(G, A) maps injectively under restriction maps into a direct sum of H2(H, A) where H runs over subgroups of k-rational points of rank 1 algebraic groups. Finally, we discuss an approach to the unsolved problem as to whether the group H2top(SL(1,D), R/Z) for a division algebra D over a p-adic field k has order equal to the number of p-power roots of unity in k.