Group Theory Classification! |G|=p ⇒ G is Cyclic (p is Prime) | Prove with Lagrange's Theorem
In Abstract Algebra, if G is a group with order p, where p is prime, then G is a cyclic group. We prove this with Lagrange's Theorem. It turns out that this completely classifies groups of prime order, because they are all isomorphic to the additive group of integers mod p: ℤp={0,1,2,3,...,p-1} (group operation is addition modulo p).
#GroupTheory #AbstractAlgebra #CyclicGroup #LagrangeTheorem
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.