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}.)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...
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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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