Let
G
G
be a countable group which is not inner amenable. Then the II
1
_{1}
-factor
M
M
is full in the following cases: (1)
M
M
is given by the group measure space construction from a triple
(
X
,
μ
,
G
)
(X,\mu ,G)
with respect to a strongly ergodic measure preserving action of
G
G
on a probability space
(
X
,
μ
)
(X,\mu )
. (2)
M
M
is the crossed product of a full II
1
_{1}
-factor by
G
G
with respect to an action.