A finite group is $[G:H]$ equal-sized cosets of $H$.Suggest a slogan
Let \(G\) be a finite group, let \(H\leq G\) be a subgroup, and let \(G/H\) be the set of left cosets of \(H\) in \(G\), so that \([G:H] = \size (G/H)\) is the index of \(H\). Then \[ \size G = [G:H]\, \size H, \qquad\text{equivalently}\qquad [G:H] = \frac{\size G}{\size H}. \]
Guide Appearances
Backlinks
C-XRC67Coset counting formula $\# G = [G:H]\,\#H$variant-of