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This paper is concerned with the Lie superalgebra S(n, m) of special type over a field of prime characteristic. We construct the modular Lie superalgebra S(n, m) and discuss some properties of this algebra. Then the derivation superalgebra of S(n, m) is determined.

In this paper, a finite-dimensional Lie superalgebra Kn,m over a field of prime characteristic is constructed. Then, we study some properties of Kn,m. Moreover, we prove that Kn,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.