On symplectic cobordism of real projective plane

This note answers a question of V. V. Vershinin concerning the properties of Buchstaber's elements $\theta_{2i+1} (2)$ in the symplectic cobordism ring of the real projective plane. It is motivated by Roush's famous result that the restriction of these elements to the projective line is trivial, and by the relationship with obstructions to multiplication in symplectic cobordism with singularities.