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We consider the group Ss. This is a group with 8! elements. Give an example of a 7-Sylow subgroup. (a) (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.

We consider the group Ss. This is a group with 8! elements. Give an example of a 7-Sylow subgroup. (a) (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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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