Let G be a cyclic group and H be a subgroup of G. Prove that H is a normal subgroup in G and G/H is cyclic. Conversely, if G/H is cyclic does this imply G is cyclic? Prove or give counter example
Let G be a cyclic group and H be a subgroup of G. Prove that H is a normal subgroup in G and G/H is cyclic. Conversely, if G/H is cyclic does this imply G is cyclic? Prove or give counter example
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 24E: 24. Let be a cyclic group. Prove that for every normal subgroup of , is a cyclic group.
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Let G be a cyclic group and H be a subgroup of G. Prove that H is a normal
subgroup in G and G/H is cyclic. Conversely, if G/H is cyclic does this imply
G is cyclic? Prove or give counter example
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