Let
L
F
C
LFC
be the class of all locally
F
C
FC
-groups. We study the existentially closed groups in the class
L
F
C
p
LF{C_p}
of all
L
F
C
LFC
-groups
H
H
whose torsion subgroup
T
(
H
)
T(H)
is a
p
p
-group. Differently from the situation in
L
F
C
LFC
, every existentially closed
L
F
C
p
LF{C_p}
-group is already closed in
L
F
C
p
LF{C_p}
, and there exist
2
ℵ
0
{2^{{\aleph _0}}}
countable closed
L
F
C
P
LF{C_P}
-groups
G
G
. However, in the countable case,
T
(
G
)
T(G)
is up to isomorphism always a unique locally finite
p
p
-group with similar properties as the unique countable existentially closed locally finite
p
p
-group
E
p
{E_p}
.