In this paper, a finite-dimensional Lie superalgebra
K
n
,
m
over a field of prime characteristic is constructed. Then, we study some properties of
K
n
,
m
. Moreover, we prove that
K
n
,
m
is an extension of a simple Lie superalgebra, and if
m
=
n
−
1
, then it is isomorphic to a subalgebra of a restricted Lie superalgebra.
Let X be a restricted Lie superalgebra of Cartan type W, S, H or K over a field of prime characteristic. In this paper, we describe the quotients of the standard normal series of the automorphism group of X. As an application, the results above are used to discuss the p-characters of the irreducible representations for X.