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Question 2 Normal subgroups. (a) Suppose G is a group and H is a subgroup. What does it mean for H to be normal? (We had several equivalent definitions; any one of them is fine.) (b) Use part (a) to show that the centre of G, Z(G), is normal. (Recall: Z(G) = {g = G: for every x = G, xg = gx}.)

Question 2 Normal subgroups. (a) Suppose G is a group and H is a subgroup. What does it mean for H to be normal? (We had several equivalent definitions; any one of them is fine.) (b) Use part (a) to show that the centre of G, Z(G), is normal. (Recall: Z(G) = {g = G: for every x = G, xg = gx}.)

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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Question 2 Normal subgroups. (a) Suppose G is a group and H is a subgroup. What does it mean for H to be normal? (We had several equivalent definitions; any one of them is fine.) (b) Use part (a) to show that the centre of G, Z(G), is normal. (Recall: Z(G) = {g = G: for every x = G, xg = gx}.)
Transcribed Image Text:Question 2 Normal subgroups. (a) Suppose G is a group and H is a subgroup. What does it mean for H to be normal? (We had several equivalent definitions; any one of them is fine.) (b) Use part (a) to show that the centre of G, Z(G), is normal. (Recall: Z(G) = {g = G: for every x = G, xg = gx}.)
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