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

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