30. Suppose that G is an Abelian group of order 16, and in computing the orders of its elements, you come across an element of order 8 and two elements of order 2. Explain why no further computations are needed to determine the somorphism class of G.

30. Suppose that G is an Abelian group of order 16, and in computing the orders of its elements, you come across an element of order 8 and two elements of order 2. Explain why no further computations are needed to determine the somorphism class of G.

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 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...

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300Can someone please help me understand the following problem. I need to know how to start the problem. i need to know the theorems identities, please thank you.

30. Suppose that G is an Abelian group of order 16, and in computing
the orders of its elements, you come across an element of order 8
and two elements of order 2. Explain why no further computations
are needed to determine the somorphism class of G.

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