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2. An element is called a square if it can be expressed in the form 6² for some b. Suppose that G is an abelian group and H is a subgroup of G. If every element of H is a square and every element of G/H is a square, prove that every element of G is a square.

2. An element is called a square if it can be expressed in the form 6² for some b. Suppose that G is an abelian group and H is a subgroup of G. If every element of H is a square and every element of G/H is a square, prove that every element of G is a square.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 12E
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2. An element is called a square if it can be expressed in the form b² for some b. Suppose that G is an abelian group and H is a subgroup of G. If every element of H is a square and every element of G/H is a square, prove that every element of G is a square.
Transcribed Image Text:2. An element is called a square if it can be expressed in the form b² for some b. Suppose that G is an abelian group and H is a subgroup of G. If every element of H is a square and every element of G/H is a square, prove that every element of G is a square.
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