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Deepak Patra posted an Question
January 06, 2022 • 23:18 pm
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30 points
30 points
- IIT JAM
- Mathematics (MA)
Please explain the marked part ..where did h' came from????????¿??example 5 let h be a normal subgroup of a group g and k be any subgroup of g. then hk = {hk i
please explain the marked part ..where did h' came from????????¿??EXAMPLE 5 Let H be a normal subgroup of a group G and K be any subgroup of G. Then HK = {hk I h E H, kE K} is a subgroup of G. To verify this, note that e = ee is in HK. Then for any a = h,k, and b = h,k, where h, h, are in H and k,, k, are in K, there is an element h' in H such that abrl = h,k,A ,-' = h,6,k-h,"l = h,h0k,k,-) So, ab is in HK.
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