3. Let G = Z20 and H =<5>, a. Find the index of H in G. b. List the elements of G/H. Construct a Cayley Table for G/H d. Find the order of the elements 3+<5> and 14+<5> e. Is G/H cyclic? Justify.
3. Let G = Z20 and H =<5>, a. Find the index of H in G. b. List the elements of G/H. Construct a Cayley Table for G/H d. Find the order of the elements 3+<5> and 14+<5> e. Is G/H cyclic? Justify.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 48E
Question

Transcribed Image Text:3. Let G = Z20 and H =<5>,
a. Find the index of H in G.
b. List the elements of G/H.
Construct a Cayley Table for G/H
d. Find the order of the elements 3+<5> and 14+<5>
e.
Is G/H cyclic? Justify.
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