5. Let H and K be normal subgroups of a group G such that H nK = {1}. Show that hk = kh for all h e H, k E K. (Hint: consider hkh-k-1.)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 20E
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5. Let H and K be normal subgroups of a group G such that H nK = {1}. Show that
hk = kh for all h e H, k E K. (Hint: consider hkh-k-1.)
Transcribed Image Text:5. Let H and K be normal subgroups of a group G such that H nK = {1}. Show that hk = kh for all h e H, k E K. (Hint: consider hkh-k-1.)
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