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6.10 Find all subgroups of Z,XZ4. 6.11 Find all subgroups of Z,xZ,>

6.10 Find all subgroups of Z,XZ4. 6.11 Find all subgroups of Z,xZ,>

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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Only 6.10 please.
### Exercise Questions **6.10** Find all subgroups of \( \mathbb{Z}_2 \times \mathbb{Z}_4 \). **6.11** Find all subgroups of \( \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2 \). **6.12** Let \( G \) and \( H \) be finite groups. Show that if \( G \times H \) is cyclic, then (i) \( G \) and \( H \) are both cyclic, and (ii) every subgroup of \( G \times H \) is of the form \( A \times B \) for some subgroups \( A \) of \( G \) and \( B \) of \( H \).
Transcribed Image Text:### Exercise Questions **6.10** Find all subgroups of \( \mathbb{Z}_2 \times \mathbb{Z}_4 \). **6.11** Find all subgroups of \( \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2 \). **6.12** Let \( G \) and \( H \) be finite groups. Show that if \( G \times H \) is cyclic, then (i) \( G \) and \( H \) are both cyclic, and (ii) every subgroup of \( G \times H \) is of the form \( A \times B \) for some subgroups \( A \) of \( G \) and \( B \) of \( H \).
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