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A group G is isomorphic to a group G̅ if there is an isomorphism φ: G → G̅. This is an equivalence relation on the collection (class) 𝓖 of all groups. We prove this by showing it satisfies: 1) reflexive property, 2) symmetric property, and 3) transitive property. Isomorphism functions are one-to-one, onto, and operation-preserving. These are the facts that need to be verified about the functions that are constructed. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: / billkinneymath 🔴 Follow me on Instagram: / billkinneymath 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.