We analyzed the luminosity-temperature-mass of gas (LX−T−Mg) relations for a sample of 21 Chandra galaxy clusters. We used the standard approach (β−model) to evaluate these relations for our sample that differs from other catalogues since it considers galaxy clusters at higher redshifts (0.4<z<1.4). We assumed power-law relations in the form \documentclass[12pt]{minimal}
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\begin{document}$L_{X} \sim(1 +z)^{A_{L_{X}T}} T^{\beta_{L_{X}T}}$\end{document}, \documentclass[12pt]{minimal}
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\begin{document}$M_{g} \sim(1 + z)^{A_{M_{g}T}} T^{\beta_{M_{g}T}}$\end{document}, and \documentclass[12pt]{minimal}
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\begin{document}$M_{g} \sim(1 + z)^{A_{M_{g}L_{X}}} L^{\beta_{M_{g}L_{X}}}$\end{document}. We obtained the following fitting parameters with 68 % confidence level: \documentclass[12pt]{minimal}
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\begin{document}$A_{L_{X}T} = 1.50 \pm0.23$\end{document}, \documentclass[12pt]{minimal}
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\begin{document}$\beta_{L_{X}T} = 2.55 \pm0.07$\end{document}; \documentclass[12pt]{minimal}
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\begin{document}$A_{M_{g}T} = -0.58 \pm0.13$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$\beta_{M_{g}T} = 1.77 \pm0.16$\end{document}; \documentclass[12pt]{minimal}
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\begin{document}$A_{M_{g}L_{X}} \approx-1.86 \pm0.34$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$\beta_{M_{g}L_{X}} = 0.73 \pm0.15$\end{document}, respectively. We found that the evolution of the Mg−T relation is small, while the Mg−LX relation is strong for the cosmological parameters Ωm=0.27 and ΩΛ=0.73. In overall, the clusters at high-z have stronger dependencies between LX−T−Mg correlations, than those for clusters at low-z. For most of galaxy clusters (first of all, from MACS and RCS surveys) these results are obtained for the first time.
