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In abstract algebra, one of the most common ways of showing that two groups are isomorphic is by defining an appropriate holnomorphism φ and then deriving an isomorphism via G/Fer ) 6(G). Use this idea to do the next problem: . Prove that Z/62 zin 2, defined by ф(n)-n mod 6 for all n E Z.) Zg. (The notation 6Z denotes {n 6m for some m E Z).) (Hint : consider the function ф : Z Definition: We say that groups are isomorphic if there exists an isomorphism between them. If G and H are isomorphic groups, we write in symbols GH Definition: Suppose G is a group, and H a normal subgroup of G. The group consisting of the set G/H with operation defined by (aH (bH) (ab) is called the quotient group of G by H. (Sometime the ter factor group" is used in place of "quotient group".)

In abstract algebra, one of the most common ways of showing that two groups are isomorphic is by defining an appropriate holnomorphism φ and then deriving an isomorphism via G/Fer ) 6(G). Use this idea to do the next problem: . Prove that Z/62 zin 2, defined by ф(n)-n mod 6 for all n E Z.) Zg. (The notation 6Z denotes {n 6m for some m E Z).) (Hint : consider the function ф : Z Definition: We say that groups are isomorphic if there exists an isomorphism between them. If G and H are isomorphic groups, we write in symbols GH Definition: Suppose G is a group, and H a normal subgroup of G. The group consisting of the set G/H with operation defined by (aH (bH) (ab) is called the quotient group of G by H. (Sometime the ter factor group" is used in place of "quotient group".)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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In abstract algebra, one of the most common ways of showing that two groups are isomorphic is by defining an appropriate holnomorphism φ and then deriving an isomorphism via G/Fer ) 6(G). Use this idea to do the next problem: . Prove that Z/62 zin 2, defined by ф(n)-n mod 6 for all n E Z.) Zg. (The notation 6Z denotes {n 6m for some m E Z).) (Hint : consider the function ф : Z Definition: We say that groups are isomorphic if there exists an isomorphism between them. If G and H are isomorphic groups, we write in symbols GH Definition: Suppose G is a group, and H a normal subgroup of G. The group consisting of the set G/H with operation defined by (aH (bH) (ab) is called the quotient group of G by H. (Sometime the ter factor group" is used in place of "quotient group".)
Transcribed Image Text:In abstract algebra, one of the most common ways of showing that two groups are isomorphic is by defining an appropriate holnomorphism φ and then deriving an isomorphism via G/Fer ) 6(G). Use this idea to do the next problem: . Prove that Z/62 zin 2, defined by ф(n)-n mod 6 for all n E Z.) Zg. (The notation 6Z denotes {n 6m for some m E Z).) (Hint : consider the function ф : Z Definition: We say that groups are isomorphic if there exists an isomorphism between them. If G and H are isomorphic groups, we write in symbols GH Definition: Suppose G is a group, and H a normal subgroup of G. The group consisting of the set G/H with operation defined by (aH (bH) (ab) is called the quotient group of G by H. (Sometime the ter factor group" is used in place of "quotient group".)
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