Use Lagrange's Theorem to show that if G has prime order, then G is cyclic. Even better, show that for every g = G, ge, we have G = (g).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 32E: Prove statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.
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(3) Use Lagrange's Theorem to show that if G has prime order, then G is cyclic. Even better, show that for every g = G,
ge, we have G = (g).
Transcribed Image Text:(3) Use Lagrange's Theorem to show that if G has prime order, then G is cyclic. Even better, show that for every g = G, ge, we have G = (g).
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