Contemporary Abstract Algebra
9th Edition
ISBN: 9781337249560
Author: Joseph Gallian
Publisher: Cengage Learning US
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Chapter 9, Problem 9E
Prove that if H has index 2 in G, then H is normal in G. (This exerciseis referred to in Chapters 24 and 25 and this chapter.)
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Chapter 9 Solutions
Contemporary Abstract Algebra
Ch. 9 - Let H={(1),(12)} . Is H normal in S3 ?Ch. 9 - Prove that An is normal in Sn .Ch. 9 - Let H={[ab0d]|a,b,dR,ad0} .IsH a normal subgroupof...Ch. 9 - Let G=GL(2,R) and let K be a subgroup of R*. Prove...Ch. 9 - Viewing 3and12 as subgroups of Z, prove that 3/12...Ch. 9 - Prove that if H has index 2 in G, then H is normal...Ch. 9 - Prove that a factor group of a cyclic group is...Ch. 9 - Prove that a factor group of an Abelian group is...Ch. 9 - Prob. 17ECh. 9 - Determine the order of (ZZ)/(2,2) . Is the group...
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