Cosets, Lagrange’s theorem and normal subgroups
equivalence relation ‘ (mod H), is denoted G=H. Right cosets Hg= fhg: h2Hgare similarly de ned. They are equiva-lence relations for the equivalence relation r (mod H) de ned by: g 1 rg 2 (mod H) if g 2g 1 1 2H, or equivalently if there exists an h2Hsuch that g 2g 1 1 = h, i.e. if g 2 = hg 1 for some h2H. The set of all equivalence classes
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