Theorem: Simon n=2 hidden-subgroup {0, s} has |G|=4, |N|=2, |G/N|=2; Lagrange |G|=|N|*|G/N|

Theorem (Simon 2-bit Lagrange factorisation + complexity gap): for G = (Z/2Z)^2 with hidden subgroup N = {(0,0), (1,1)}, the Lagrange structure is: |G| = 4, |N| = 2, |G/N| = |G| / |N| = 2. Lagrange's theorem for abelian groups: |G| = |N| *…