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Question 7: For any group G, prove that G’ is the set of all ‘long commutators’
Question 7: For any group G, prove that G’ is the set of all ‘long commutators’
11
1212
'{......|2}
nni
GaaaaaaaGandn
--
ºÎ³
Solution: Let G be a group. Here,
i
aG
Î
. Therefore, a, b, c, d also belong to G.
Or,
,,,
abcdG
Î
.
Then the commutator of a, b, c and d is the elements a-1, b-1, c-1 and d-1

11
1212
'{......|2}
nni
GaaaaaaaGandn
--
ºÎ³
Here, each ai is a commutator in G.
C is the collection of all finite...