Let G is a linear algebraic group over algebraic closed field, B is an Borel subgroup of G. Does there exist g$\in$G which is only in a finite numbers of conjugates of B (they are also Borel subgroups) ?
I choose this version of condition from the book:Tauvel, Patrice, and W. T. Rupert. Lie algebras and algebraic groups 28.2.1.
It appears in the lemma before the density theorem of Borel subgroups, but I do not see any book do this for Borel subgroups directly, they all do it for Cartan subgroups, choosing a semisimple regular element of the unique maximal torus, but Borel subgroups are bigger, maybe they have more intersections.
The similar question is at here with no answer: https://math.stackexchange.com/questions/3113958/element-in-finite-number-of-borel-subgroups