CS202/2005/Schedule/2005-11-07

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Still more GroupTheory: Lagrange's Theorem on the size of subgroups. Cosets, normal subgroups and quotient groups. Readings: §20.8.

More detail:

Cosets of a subgroup; definition, proof that they are all the same size and partition the group (which implies Lagrange's Theorem that the order of a subgroup divides the order of a group).
Applications: no nontrivial proper subgroups for ℤ_p, exactly p+1 nontrivial proper subgroups for D_p.
Normal subgroups, congruence modulo a subgroup, and quotient groups.