| Abstract:
Every irreducible conic admits a group law - very similar to group laws on
elliptic curves. In this talk, we explore some of the properties of these
groups and classify them according to the conics from which they are
constructed. Then we compare these group laws with those arising from
non-singular cubic curves. Ovals being very close to conics, it is natural
to ask whether ovals admit a natural group law. We show some examples of
algebraic ovals having group laws very similar to that of conics. It is an
open problem for general ovals.
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