We analyzed the luminosity-temperature-mass of gas (L_{X} - T - M_{g}) relation for sample of galaxy clusters that have been observed by the Chandra satellite. We used 21 high-redshift clusters (0.4 < z < 1.4). We assumed a power-law relation between the X-ray luminosity of galaxy clusters and its temperature and redshift L_{X} ~ (1+z)^{A_{L_{X}T}}T^{beta_{L_{X}T}}. We obtained that for an Omega_{m} = 0.27 and Lambda = 0.73 universe, A_{L_{X}T} = 1.50 +/- 0.23, beta_{L_{X}T} = 2.55 +/- 0.07 (for 68% confidence level). Then, we found the evolution of M_{g} - T relation is small. We assumed a power-law relation in the form M_{g} ~ (1+z)^{A_{M_{g}T}}T^{beta_{M_{g}T}} also, and we obtained A_{M_{g}T} = -0.58 +/- 0.13 and beta_{M_{g}T} = 1.77 +/- 0.16. We also obtained the evolution in M_{g} - L_{X} relation, we can conclude that such relation has strong evolution for our cosmological parameters. We used M_{g} ~ (1+z)^{A_{M_{g}L_{X}}}L^{beta_{M_{g}L_{X}}} equation for assuming this relation and we found A_{M_{g}L_{X}} ~ -1.86 +/- 0.34 and beta_{M_{g}L_{X}} = 0.73 +/- 0.15 for Omega_{m} = 0.27 and Lambda = 0.73 universe. In overal, the clusters on big redshifts have much stronger evolution between correlations of luminosity, temperature and mass, then such correlations for clusters at small redshifts. We can conclude that such strong evolution in L_{X} - T - M_{g} correlations indicate that in the past the clusters have bigger temperature and higher luminosity.
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