Mehdi Jafari - Department of Mathematics, Payame Noor University, P.O. Box۱۹۳۹۵- ۳۶۹۷, Tehran, Iran
Amirhesam Zaeim - Department of Mathematics, Payame Noor University, P.O. Box۱۹۳۹۵- ۳۶۹۷, Tehran, Iran
Amin Tanhaeivash - Department of Mathematics, Payame Noor University, P.O. Box۱۹۳۹۵- ۳۶۹۷, Tehran, Iran

In this paper, by applying the Lie symmetry method we will obtain the lie symmetry group of the Fitnessequation. Also the one dimensional optimal system of Lie algebra is obtained. Using the optimal system,similarity reductions of this equation will be constructed and some group invariant solutions are obtained.

Lie symmetries, Lie symmetry group, Infinitesimal generators, Optimal System