  Let $G$ be a compact Lie group of Lie type $B_{n},$ such as $SO(2n+1)$. We
characterize the tuples\ $(x_{1},...,x_{L})$ of the elements $x_{j}\in G$ which
have the property that the product of their conjugacy classes has non-empty
interior. Equivalently, the convolution product of the orbital measures
supported on their conjugacy classes is absolutely continuous with respect to
Haar measure. The characterization depends on the dimensions of the largest
eigenspaces of each $x_{j}$. Such a characterization was previously only known
for the compact Lie groups of type $A_{n}$.
