Tag: Group theory

• Normal Subgroups and Quotient Groups: The Condition for Multiplying CosetsFrom the wish to multiply cosets by their representatives we derive normality, prove that G/N is a group with a natural surjection onto it, and work out Z/nZ in full detail.MathematicsAlgebra: Groups, Rings and FieldsUndergraduateGroup theoryNormal subgroupsQuotient groupsCosetsCongruences~32 min
• Subgroups and Cosets: Why Lagrange's Theorem Produces DivisibilityFrom the one-step subgroup test to Lagrange's theorem: left cosets split a group into blocks of equal size, giving Euler's theorem and a counterexample to the converse.MathematicsAlgebra: Groups, Rings and FieldsUndergraduateGroup theorySubgroupsCosetsLagrange's theoremFinite groups~34 min