One-parameter group
In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism φ : R → G {\displaystyle \varphi :\mathbb {R} \rightarrow G} from the real line R {\displaystyle \mathbb {R} } (as an additive group) to some other topological group G {\displaystyle G} . If φ {\displaystyle \varphi } is injective then φ ( R ) {\displaystyle \varphi (\mathbb {R} )} , the image, will be a subgroup of G {\displaystyle G} that is isomorphic to R {\displaystyle \mathbb {R} } as an additive group.