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Problem 86 (Lagrange's Theorem Proof)

Prove Lagrange's Theorem.

Theorem (Lagrange's Theorem)

Suppose that $G$ is a finite group and that $H$ is a subgroup of $G$. Then the order of $H$ divides the order of $G$. In particular, we know that $|G|/|H|$ equals the number of distinct right (or left) cosets of $H$ in $G$.

The following pages link to this page.

Problem.LagrangesTheoremProof
Schedule.20161116
Schedule.20161118
Schedule.20161121
Schedule.20161128
Schedule.20171117
Schedule.20171127
Schedule.AllProblems
Solution.LagrangesTheoremProofLevi
Solution.LagrangesTheoremProofTyler

Solution.LagrangesTheoremProofLevi
Solution.LagrangesTheoremProofTyler

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Page last modified on December 04, 2019, at 05:18 PM

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HomePage Current Problems All Problems Pictures ProblemsByWeek List of Problems List of Definitions List of Theorems List of Conjectures All Recent changes (use this to find a page that may have been lost)	Problem Lagrange's Theorem Proof Please Login to access more options. Problem 86 (Lagrange's Theorem Proof) Prove Lagrange's Theorem. Theorem (Lagrange's Theorem) Suppose that $G$ is a finite group and that $H$ is a subgroup of $G$. Then the order of $H$ divides the order of $G$. In particular, we know that $\|G\|/\|H\|$ equals the number of distinct right (or left) cosets of $H$ in $G$. The following pages link to this page. Problem.LagrangesTheoremProof Schedule.20161116 Schedule.20161118 Schedule.20161121 Schedule.20161128 Schedule.20171117 Schedule.20171127 Schedule.AllProblems Solution.LagrangesTheoremProofLevi Solution.LagrangesTheoremProofTyler Solution.LagrangesTheoremProofLevi Solution.LagrangesTheoremProofTyler Edit Page History Source Attach File Backlinks List Group Page last modified on December 04, 2019, at 05:18 PM
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