---- > [!definition] Definition. ([[index of a subgroup]]) > Fix a [[group]] $G$ and a [[subgroup]] $K$. The **index of $K$ in $G$** is the total number of *distinct* right $K$-[[coset|cosets]] of $K$ in $G$. We write this index $[G:K]$. > \ > (We can equivalently define in terms of left [[coset|cosets]] since the total number of left [[coset]]s always equals the total number of right [[coset]]s.) ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```