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(b) Let G be a group with N, K as subgroups of G. Define NK = {nk | n € N, ke K} (i) If N is a normal subgroup of G, then prove that NK is a subgroup of G (ii) If both N, K are normal subgroups of G, then prove that NK is a normal subgroup of G

(b) Let G be a group with N, K as subgroups of G. Define NK = {nk | n € N, ke K} (i) If N is a normal subgroup of G, then prove that NK is a subgroup of G (ii) If both N, K are normal subgroups of G, then prove that NK is a normal subgroup of G

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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(b) Let G be a group with N, K as subgroups of G. Define NK = {nk | n € N, ke K} (i) If N is a normal subgroup of G, then prove that NK is a subgroup of G (ii) If both N, K are normal subgroups of G, then prove that NK is a normal subgroup of G
Transcribed Image Text:(b) Let G be a group with N, K as subgroups of G. Define NK = {nk | n € N, ke K} (i) If N is a normal subgroup of G, then prove that NK is a subgroup of G (ii) If both N, K are normal subgroups of G, then prove that NK is a normal subgroup of G
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