Assertion: abelian group's subgroup | /r/HasProperty | obtained
Facets:
value: by considering α a complex variable
type: MANNER
Source sentences:
text: (If β, θ vary independently, then a two-dimensional abelian subgroup is obtained, consisting of simultaneous rotations about the z axis and boosts along the z-axis; in contrast, the one-dimensional subgroup discussed here consists of those elements of this two-dimensional subgroup such that the rapidity of the boost and angle of the rotation have a fixed ratio.)
text: This generates a two-parameter abelian subgroup, which is obtained by considering α a complex variable rather than a constant.
text: An even more general idea than that of subgroup-defining functions is the following: any subgroup that is obtained by starting from a collection of normal subgroups and using deterministic processes, which may involve joins, intersections, centralizers, and commutators, or other processes, still yields a normal subgroup.