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We study the class of 3-dimensional nonlinear 2-hessian equations mentionedin the text. We perform preliminary group classification on 2-hessian equation.In fact, we find additional equivalence transformation on the space(x,y,z,u,f), with the aid of a method, then we take their projections on thespace (x,y,z,f), so we prove an optimal system of one-dimensional Lie subalgebras of this equation is generated by A1 to A12, which introduced intheorem 2, ultimately, A number of new interesting nonlinear invariant modelsare obtained which have non-trivial in variance algebras. The result of theseworks is a wide class of equations which summarized in table. So at the end ofthis work, some exact solutions of 2-hessian equation are presented. The paperis one of the few applications of an algebraic approach to the groupclassification using Lie method.

Preliminary Group Classification and some exact solutions of 2Hessian equation