MathDB
Problems
Contests
Undergraduate contests
Putnam
1975 Putnam
B1
B1
Part of
1975 Putnam
Problems
(1)
Putnam 1975 B1
Source: Putnam 1975
2/17/2022
Consider the additive group
Z
2
\mathbb{Z}^{2}
Z
2
. Let
H
H
H
be the smallest subgroup containing
(
3
,
8
)
,
(
4
,
−
1
)
(3,8), (4,-1)
(
3
,
8
)
,
(
4
,
−
1
)
and
(
5
,
4
)
(5,4)
(
5
,
4
)
. Let
H
x
y
H_{xy}
H
x
y
be the smallest subgroup containing
(
0
,
x
)
(0,x)
(
0
,
x
)
and
(
1
,
y
)
(1,y)
(
1
,
y
)
. Find some pair
(
x
,
y
)
(x,y)
(
x
,
y
)
with
x
>
0
x>0
x
>
0
such that
H
=
H
x
y
H=H_{xy}
H
=
H
x
y
.
Putnam
group theory
abstract algebra