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Prove that if H and K are subgroups of a group G with operatio: Question 8. then HnK is a subgroup of G. Let H = {(1), (1 2)} and K = {(1), (1 2 3), (1 3 2)}. Both H K are subgroups of S3. Show that HUK is not a subgroup of S3. It follows that a unio: subgroups is not necessarily a subgroup.

Prove that if H and K are subgroups of a group G with operatio: Question 8. then HnK is a subgroup of G. Let H = {(1), (1 2)} and K = {(1), (1 2 3), (1 3 2)}. Both H K are subgroups of S3. Show that HUK is not a subgroup of S3. It follows that a unio: subgroups is not necessarily a subgroup.

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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Prove that if H and K are subgroups of a group G with operation *, Question 8. then HNK is a subgroup of G. Let H = {(1), (1 2)} and K = {(1), (1 2 3), (1 3 2)}. Both H and K are subgroups of S3. Show that HUK is not a subgroup of S3. It follows that a union of subgroups is not necessarily a subgroup.
Transcribed Image Text:Prove that if H and K are subgroups of a group G with operation *, Question 8. then HNK is a subgroup of G. Let H = {(1), (1 2)} and K = {(1), (1 2 3), (1 3 2)}. Both H and K are subgroups of S3. Show that HUK is not a subgroup of S3. It follows that a union of subgroups is not necessarily a subgroup.
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