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We consider two families of finite-dimensional simple Lie superalgebras ofCartan type, denoted by HO and KO, over an algebraically closed field ofcharacteristic p>3. Using the weight space decompositions and the principalgradings we first show that neither HO nor KO possesses a nondegenerateassociative form. Then, by means of computing the superderivations from the Liesuperalgebras in consideration into their dual modules, the second cohomologygroups with coefficients in the trivial modules are proved to be vanishing.

Associative forms and second cohomologies of Lie superalgebras $HO$ and $KO$