Proposition 2.28
(Bogolyubov in a general finite abelian group)
.
Assuming that:
A
⊆
G
of density
α
>
0
Then
there exists
Γ
⊆
G
^
of size at most
2
α
−
2
such that
A
+
A
−
A
−
A
⊇
B
(
Γ
,
ρ
)
.