Math 441 - Abstract Algebra - Problem - PowersOfProductsInAnAbelianGroup

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Problem 57 (Powers Of Products In An Abelian Group)

Suppose $G$ is an Abelian group. Prove that if $a,b\in G$, then $(ab)^2=a^2b^2$. Then use induction to prove that if $a,b\in G$, then $(ab)^n=a^nb^n$ for each $n\in \mathbb{N}$.

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Problem.PowersOfProductsInAnAbelianGroup
Schedule.20161014
Schedule.20161017
Schedule.20171013
Schedule.20171016
Schedule.20171020
Schedule.20171023
Schedule.20171025
Schedule.20171027
Schedule.AllProblems
Solution.PowersOfProductsInAnAbelianGroupLevi

Solution.PowersOfProductsInAnAbelianGroupLevi

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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 Powers Of Products In An Abelian Group Please Login to access more options. Problem 57 (Powers Of Products In An Abelian Group) Suppose $G$ is an Abelian group. Prove that if $a,b\in G$, then $(ab)^2=a^2b^2$. Then use induction to prove that if $a,b\in G$, then $(ab)^n=a^nb^n$ for each $n\in \mathbb{N}$. The following pages link to this page. Problem.PowersOfProductsInAnAbelianGroup Schedule.20161014 Schedule.20161017 Schedule.20171013 Schedule.20171016 Schedule.20171020 Schedule.20171023 Schedule.20171025 Schedule.20171027 Schedule.AllProblems Solution.PowersOfProductsInAnAbelianGroupLevi Solution.PowersOfProductsInAnAbelianGroupLevi Edit Page History Source Attach File Backlinks List Group Page last modified on November 01, 2018, at 02:42 PM
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