Lagrange theorem |G| = [G:H] |H|; Z_6 / Z_3 index 2

Lagrange theorem framework for finite groups (Lagrange 1771; Cauchy 1844). Setup: for a finite group G with subgroup H subseteq G, the order |H| divides |G|, with quotient [G:H] = |G|/|H| = number of left/right cosets - the *index* of H in…