The group table of a group G is shown below. e a b C d b b a e h b f e e e C d a a ff b C 9 9 C d h h d a C d f g h df g h f d C b d C 9 g f e h h g f d The subset J = 9 h e a b C a a b с e b h a 9 b h e с d a e f f g {e, b} is a subgroup of G. (a) List all the distinct left cosets and all the distinct right cosets of J in G. (b) State whether J is normal in G, briefly justifying your answer.
The group table of a group G is shown below. e a b C d b b a e h b f e e e C d a a ff b C 9 9 C d h h d a C d f g h df g h f d C b d C 9 g f e h h g f d The subset J = 9 h e a b C a a b с e b h a 9 b h e с d a e f f g {e, b} is a subgroup of G. (a) List all the distinct left cosets and all the distinct right cosets of J in G. (b) State whether J is normal in G, briefly justifying your answer.
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 13E: Let H be a subgroup of the group G. Prove that if two right cosets Ha and Hb are not disjoint, then...
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Transcribed Image Text:The group table of a group G is shown below.
df g h
h
b
e
a
b
C
d
b C
b
a e
h
9
b f e h
g f e
h g f
d
e a
e
C
d
a
ff b C
d
9
9 C
h h d a
C
The subset J =
a
b
dfg
f d
9
h
e
a
b
C
a 9
b h
с e
C
d
a
b
h
C
d
a
e
e
f
f g
{e, b} is a subgroup of G.
(a) List all the distinct left cosets and all the distinct right cosets of J in G.
(b) State whether J is normal in G, briefly justifying your answer.
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