a) List all subgroups of G and prove that you have found them all. b) Determine the centre of G. Write the elements c)Find a non-trivial, proper normal subgroup of G.
a) List all subgroups of G and prove that you have found them all. b) Determine the centre of G. Write the elements c)Find a non-trivial, proper normal subgroup of G.
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
a) List all subgroups of G and prove that you have found them all.
b) Determine the centre of G. Write the elements
c)Find a non-trivial, proper normal subgroup of G.

Transcribed Image Text:6.
This question concerns the group (G, *) given by the following Cayley table.
a
f g
C
k d
b C
db
fb g h
dh
b
a b
C
d
k
C
h
g
a
C dk f
h k
d
9
hk a
a
k b
с
d
k
b
k
с
a
a 9
fh g
6498
h
f
g h
d b
f g
a
g
h
k
a C
b
d b
h
a
d
C k
с
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