I need help with number 1 1. Up to isomorphism, how many different abelian groups with 800 elements exist? List them.(This is an exercise in using the Fundamental Theorem of Abelian Groups.)We consider the group Sg. This is a group with 8! elements.(a)Give an example of a 7-Sylow subgroup.(b) How many 7-Sylow subgroups exist in Sg? Explain your answer. (I am not asking you toapply Sylow's Theorem here that occurs in (c). Here, you will be thinking very specifically about2.

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Up to isomorphism, how many different abelian groups with 800 elements exist? List them. s is an exercise in using the Fundamental Theorem of Abelian Groups.)

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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I need help with number 1

1. Up to isomorphism, how many different abelian groups with 800 elements exist? List them.
(This is an exercise in using the Fundamental Theorem of Abelian Groups.)
We consider the group Sg. This is a group with 8! elements.
(a)
Give an example of a 7-Sylow subgroup.
(b) How many 7-Sylow subgroups exist in Sg? Explain your answer. (I am not asking you to
apply Sylow's Theorem here that occurs in (c). Here, you will be thinking very specifically about
2.

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