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1. Show that H={[0], [2], [4]} is a subgroup of a group (Z6+6). Obtain all the distinct left cosets of H in Z.

1. Show that H={[0], [2], [4]} is a subgroup of a group (Z6+6). Obtain all the distinct left cosets of H in Z.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 10E: Let be a subgroup of a group with . Prove that if and only if .
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1. Show that H = {[0],[2].[4]} is a subgroup of a group (Z,+6). Obtain all the distinct left cosets of H in Z,.
Transcribed Image Text:1. Show that H = {[0],[2].[4]} is a subgroup of a group (Z,+6). Obtain all the distinct left cosets of H in Z,.
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