Editing Orthogonal group (section)

=== Lie subgroups ===
In physics, particularly in the areas of [[Kaluza–Klein]] compactification, it is important to find out the subgroups of the orthogonal group. The main ones are:
: <math>\mathrm{O}(n) \supset \mathrm{O}(n - 1)</math> – preserve an axis
: <math>\mathrm{O}(2n) \supset \mathrm{U}(n) \supset \mathrm{SU}(n)</math> – {{math|U(''n'')}} are those that preserve a compatible complex structure ''or'' a compatible symplectic structure – see [[Unitary group#2-out-of-3 property|2-out-of-3 property]]; {{math|SU(''n'')}} also preserves a complex orientation.
: <math>\mathrm{O}(2n) \supset \mathrm{USp}(n)</math>
: <math>\mathrm{O}(7) \supset \mathrm{G}_2</math>