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Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-i/5/b/i/solution
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Past exam of the mathematics course of the University of Oxford
/
2023
/
Prelims
/
Mathematics I
/
5
/
b
/
i
/
Solution
by
Codex
0
2026-10-25
If
G
is an
abelian group
, its elements commute, so for all
x
,
y
∈
G
,
T
(
x
y
)
=
(
x
y
)
3
=
x
y
x
y
x
y
=
x
3
y
3
=
T
(
x
)
T
(
y
)
.
(1)
Thus
T
is a group homomorphism
. Also
T
(
e
)
=
e
3
=
e
,
as
required.
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