
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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I need help with number 3

Transcribed Image Text:(f) Use Sylow's Theorem to show why every 8-cycle is contained in some 2-Sylow subgroup,
and why every 2-Sylow subgroup of S8 has to contain an 8-cycle.
(g) Find an 8-cycle in the 2-Sylow subgroup I described for you! Explain your answer.
3. Let G be a finite group, and suppose that N is a normal subgroup of G. Suppose that P is a
p-Sylow subgroup of N. (This will not necessarily be a p-Sylow subgroup of G.) Suppose that P is
normal in N. Prove that P is normal in G. (This should be short ... just be clear in your proof.)
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