Editing Homotopy groups of spheres (section)

===Stable and unstable groups===
The fact that the groups below the jagged line in the table above are constant along the diagonals is explained by the [[Freudenthal suspension theorem|suspension theorem]] of [[Hans Freudenthal]], which implies that the suspension homomorphism from  {{math|π<sub>''n''+''k''</sub>(''S''<sup>''n''</sup>)}} to  {{math|π<sub>''n''+''k''+1</sub>(''S''<sup>''n''+1</sup>)}} is an isomorphism for {{math|''n'' &gt; ''k'' + 1}}.  The groups {{math|π<sub>''n''+''k''</sub>(''S''<sup>''n''</sup>)}} with {{math|''n'' > ''k'' + 1}} are called the ''stable homotopy groups of spheres'', and are denoted {{math|π{{su|lh=1|b=''k''|p=''S''}}}}: they are finite abelian groups for {{math|''k'' ≠ 0}}, and have been computed in numerous cases, although the general pattern is still elusive.{{sfn|Hatcher|2002|loc=Stable homotopy groups, pp. 385–393}} For {{math|''n'' ≤ ''k''+1}}, the groups are called the ''unstable homotopy groups of spheres''.{{cn|date=February 2022}}