Let
G
G
be a finite group and
π
\pi
a set of primes. We consider the family of subgroups of
G
:
F
=
{
M
:
M
>
⋅
G
,
[
G
:
M
]
π
=
1
,
[
G
:
M
]
G:\mathcal {F} = \{ M:M > \cdot G,{[G:M]_\pi } = 1,[G:M]
is composite} and denote
S
π
(
G
)
=
⋂
{
M
:
M
∈
F
}
{S_\pi }(G) = \bigcap \left \{ M: M \in \mathcal {F} \right \}
if
F
\mathcal {F}
is non-empty, otherwise
S
π
(
G
)
=
G
{S_\pi }(G) = G
. The purpose of this note is to prove Theorem. Let
G
G
be a
π
\pi
-solvable group. Then
S
π
(
G
)
{S_\pi }(G)
has the following properties: (1)
S
π
(
G
)
/
O
π
(
G
)
{S_\pi }(G)/{O_\pi }(G)
is supersolvable. (2)
S
π
(
S
π
(
G
)
)
=
S
π
(
G
)
{S_\pi }({S_\pi }(G)) = {S_\pi }(G)
. (3)
G
/
O
π
(
G
)
G/{O_\pi }(G)
is supersolvable if and only if
S
π
(
G
)
=
G
{S_\pi }(G) = G
.