Let
G
G
be a smooth connected linear algebraic group over a field
k
k
, and let
X
X
be a
G
G
-torsor. Totaro asked: if
X
X
admits a zero-cycle of degree
d
≥
1
d \geq 1
, then does
X
X
have a closed étalé point of degree dividing
d
d
? We give an affirmative answer for absolutely simple classical adjoint groups of types
A
1
A_1
and
A
2
n
A_{2n}
over fields of characteristic
≠
2
\neq 2
.