A subset
E
E
of an infinite discrete group
G
G
is called (i) an
R
W
{R_W}
-set if any bounded function on
G
G
supported by
E
E
is weakly almost periodic, (ii) a weak
p
p
-Sidon set
(
1
≤
p
>
2
)
(1 \leq p > 2)
if on
l
1
(
E
)
{l^1}(E)
the
l
p
{l^p}
-norm is bounded by a constant times the maximal
C
∗
{C^*}
-norm of
l
1
(
G
)
{l^1}(G)
, (iii) a
T
T
-set if
x
E
∩
E
xE \cap E
and
E
x
∩
E
Ex \cap E
are finite whenever
x
≠
e
x \ne e
, and (iv) an
F
T
FT
-set if it is a finite union of
T
T
-sets. In this paper, we study relationships among these four classes of thin sets. We show, among other results, that (a) every infinite group
G
G
contains an
R
W
{R_W}
-set which is not an
F
T
FT
-set; (b) countable weak
p
p
-Sidon sets,
1
≤
p
>
4
/
3
1 \leq p > 4/3
are
F
T
FT
-sets.