Connected algebraic group

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This article defines a property that can be evaluated for an algebraic group. it is probably not a property that can directly be evaluated, or make sense, for an abstract group|View other properties of algebraic groups

Definition

An algebraic group over a field is said to be connected if it satisfies the following equivalent conditions:

  1. It is connected as a semitopological group in the Zariski topology.
  2. It has no proper open subgroup. Note that whether or not the group is connected depends only on the underlying algebraic variety.

Facts