In mathematics, specifically group theory, the identity component of a group G (also known as its unity component) refers to several closely related notions of the largest connected subgroup of G containing the identity element.
It is a subgroup since multiplication and inversion in a topological or algebraic group are continuous maps by definition.
Moreover, for any continuous automorphism a of G we have Thus, G0 is a characteristic (topological or algebraic) subgroup of G, so it is normal.
The identity component G0 of a topological group G need not be open in G. In fact, we may have G0 = {e}, in which case G is totally disconnected.
Any connected algebraic group over a non-Archimedean local field K is totally disconnected in the K-topology and thus has trivial identity component in that topology.