12:51 >) [U20 (3)]= How many cosets of A4 in S4? Today 12:42 PM [ZxZ: Zx 4Z) = Edit Suppose H is a normal subgroup of Z20 such that Z20/HZ5. Then H= 13. 14. 15. 16
12:51 >) [U20 (3)]= How many cosets of A4 in S4? Today 12:42 PM [ZxZ: Zx 4Z) = Edit Suppose H is a normal subgroup of Z20 such that Z20/HZ5. Then H= 13. 14. 15. 16
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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![The image appears to contain mathematical homework problems related to group theory. Below is the transcription of the content for educational purposes:
1. \([U_{20} : \langle 3 \rangle] =\)
Answer space: \(13.\)_____________
2. How many cosets of \(A_4\) in \(S_4\)?
Answer space: \(14.\)_____________
3. Suppose \(H\) is a normal subgroup of \(\mathbb{Z}_{20}\) such that \(\mathbb{Z}_{20} / H \cong \mathbb{Z}_5\).
Then \(H = \)
Answer space: \(15.\)_____________
4. \([\mathbb{Z} \times \mathbb{Z} : \mathbb{Z} \times 4\mathbb{Z}] =\)
Answer space: \(16.\)_____________
Each line of text includes a mathematical problem with space provided for an answer. The problems deal with cosets, subgroups, and quotient groups in algebraic structures. There are no graphs or diagrams present in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4dd9d0aa-b3c2-41ec-8a5d-b1562792e6fa%2Ff40b7262-e877-4741-9bf3-497963173962%2Fsmw6ul_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image appears to contain mathematical homework problems related to group theory. Below is the transcription of the content for educational purposes:
1. \([U_{20} : \langle 3 \rangle] =\)
Answer space: \(13.\)_____________
2. How many cosets of \(A_4\) in \(S_4\)?
Answer space: \(14.\)_____________
3. Suppose \(H\) is a normal subgroup of \(\mathbb{Z}_{20}\) such that \(\mathbb{Z}_{20} / H \cong \mathbb{Z}_5\).
Then \(H = \)
Answer space: \(15.\)_____________
4. \([\mathbb{Z} \times \mathbb{Z} : \mathbb{Z} \times 4\mathbb{Z}] =\)
Answer space: \(16.\)_____________
Each line of text includes a mathematical problem with space provided for an answer. The problems deal with cosets, subgroups, and quotient groups in algebraic structures. There are no graphs or diagrams present in the image.
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