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To determine the relative distances and peculiar velocities of 140 groups and clusters of galaxies at low redshifts ($z$ < 0.12), we used the fundamental plane (FP) of early-type galaxies (from the Sloan Digital Sky Survey (SDSS) data). We constructed the Hubble diagram for the relative distances of galaxy groups/clusters versus their radial velocities in the cosmic microwave background (CMB) reference frame in the flat $\Lambda$ cold dark matter ($\Lambda$CDM) model ($\Omega_m=0.3$, $H_0=70$~km~s$^{-1}$ Mpc$^{-1}$). We have found that the standard logarithmic deviation for groups and clusters of galaxies on the Hubble diagram (minus peculiar velocities) is $\pm0.0173$ ($N$ = 140), which corresponds to a deviation of $70\pm2.8$~km~s$^{-1}$ Mpc$^{-1}$ in the Hubble constant. For a sample of galaxy systems ($N$ = 63), the X-ray luminosity of which is in an interval of (0.151--4)~$\times 10^{44}$~erg/s, this quantity turned out to be $70\pm2.1$~km~s$^{-1}$ Mpc$^{-1}$. The root-mean-square deviations of peculiar velocities with quadratic accounting for errors are $^{1/2}$ = $714\pm7$~km/s and $600\pm7$~km/s, respectively. For five large superclusters of galaxies from the SDSS region, the average peculiar velocity relaive to the CMB reference frame is $+240\pm250$~km/s. We detected no outflow of galaxy systems from the void (Giant Void, $\alpha \approx 13^h, \delta \approx 40^\circ, z \approx 0.107$) formed by groups and clusters of galaxies., Comment: 10 pages, 5 figures. Accepted for publication in Astronomy Reports

This work is a continuation of the work of Kopylova and Kopylov (2016) to build a fundamental plane (FP) of groups and clusters of galaxies -- here a sample of galaxies systems is increased from 94 to 172 objects. We have studied the ratios between the basic characteristics of groups and clusters of galaxies according to the archival data of SDSS, 2MASX and NED catalogs. Measured parameters ($\log L_K$, $\log R_e$ and $\log \sigma$) of clusters of galaxies determine the fundamental plane in the near infrared region: $L_K \propto R_e^{0.77\pm0.09} \sigma^{1.44\pm0.12}$. The form of the FP of groups/clusters is consistent with the FP of the early -- types of galaxies (SDSS, $r$-band) determined in the same way. Direct regression relative to the padius $\log r_e$ in the kpc gives a projection of the FP -- $\log R_e=0.98(\pm0.06)\,\log \sigma-0.56(\pm0.04)<\log \langle I_e \rangle+3.57(\pm0.07)$, that can be used to determine the distances of the systems of galaxies. The root-mean-square deviation of the FP zero-point is 0.07 which is equal to the 16\% error in determining the distance of the group or cluster of galaxies. For the first time, we measured the peculiar velocities of the superclusters of galaxies. The mean peculiar velocity of the 5 superclusters of galaxies relative to the CMB is $+75\pm360$~km~s$^{-1}$., Comment: 14 pages, 7 figures, 1 table. Astrophysical Bulletin, 2024, 79, 1. Key results in Figures 6 and 7

We report the results of a study of the distribution of galaxies in the projection along the radius ($R \leq 3R_{200c}$) for 157~groups and clusters of galaxies in the local Universe (0.01 < $z$ < 0.10) with line-of-sight velocity dispersions~200~km~s$^{-1}$ < $ \sigma$ < 1100~km~s$^{-1}$. We introduce a new observed boundary for the halos of clusters of galaxies, which we identify with the splashback radius $R_{\rm{sp}}$. We also identified the core of groups/clusters of galaxies with the radius$R_c$. These radii are determined by the observed integrated distribution of the number of galaxies as a function of squared angular radius from the center of the group/cluster, which (usually) coincides with the brightest galaxy. We found for the entire sample that the boundary of dark matter $R_{\rm{sp}}$ for groups/clusters of galaxies is proportional to the radius $R_{\rm{200c}}$ of the virialized region. We measured the mean radius $\langle R_{\rm{sp}} \rangle = 1.14\pm0.02$~Mpc for groups of galaxies ($\sigma \leq 400$~km~s$^{-1}$) and $\langle R_{\rm{sp}} \rangle = 2.00\pm0.07$~Mpc for clusters of galaxies ($\sigma > 400$~km~s$^{-1}$). The mean ratio of radii is $\langle R_{\rm{sp}}/R_{\rm{200c}} \rangle = 1.40\pm0.02$}, or $\langle R_{\rm{sp}}/R_{\rm{200m}} \rangle = 0.88\pm0.02$., Comment: 15 pages, 7 figures, 2 tables. The article provides references to the X-ray luminosity of galaxy clusters and clarifies the descriptions of the columns

We present a study of the distribution of galaxies along the radius of 157 groups and clusters of galaxies (200~km~s$^{-1}$ < $\sigma$ < 1100~km~s$^{-1}$) of the local Universe (0.01 < $z$ < 0.1). We introduced a new boundary of galaxy systems and identified it with the splashback radius $R_{sp}$. We also identified the central region of galaxy systems with a radius of $R_c$. These radii are defined by the observed integrated distribution of the total number of galaxies depending on the squared distance from the center of the groups/clusters coinciding, as a rule, with the brightest galaxy. We show that the radius $R_{sp}$ is proportional to the $R_{200c}$ (radius of the virialized region of a galaxy cluster) and to the radius of the central region $R_c$ with a slope close to 1. Among the obtained dependences of the radii on X-ray luminosity, the $\log R_{sp}$ - $\log L_X$ relation has the lowest scatter. We measured $$ = $1.67\pm0.05$~Mpc for the total sample, $$ = $1.14\pm0.14$~Mpc for galaxy groups with $\sigma \leq$ 400~km~s$^{-1}$, $$ = $2.00\pm0.20$~Mpc for galaxy clusters with $\sigma$ > 400~km~s$^{-1}$. We found the average ratio of the radii $R_{sp}/R_{200c} = 1.40\pm0.02$ or $R_{sp}/R_{200m} = 0.88\pm0.02$.}, Comment: 7 pages, 3 figures, 1 table

The paper presents the results of studying the dynamics of galaxies, properties of early-type galaxies, properties of galaxies with the quenched star formation (QGs) in the A 2142 based on the archival data from the Sloan Digital Sky Survey. We found the observed halo boundary, the splashback radius $R_{sp}$, which is equal to 4.12 Mpc ($M_r < -20\,.\!\!^{\rm m}3$) and 4.06 Mpc ($M_r < -21\,.\!\!^{\rm m}3$) over the integral distribution of the number of galaxies as a function of the squared distance from the center. We have studied how early-type galaxies are distributed in the center and in the outskirts of the cluster ($R/R_{200}$ < 3, $M_r < -20\,.\!\!^{\rm m}3$) and plotted the red sequence in the form of (g - r) = $(-0.024\pm0.001)M_r + (0.441\pm0.005$). Among all the cluster galaxies, the galaxies with the quenched star formation ( $- 12\,yr^{- 1} < \log sSFR < - 10.75\,yr^{- 1}$) make up about one third. We have found that the fraction of QGs beyond the splashback $R_{sp}$ is the same as in the field at the same z with coordinates of the center of $16\,.\!\!^{\rm h}5$, $31^{\circ}$ and a size of $300'$. For galaxies with the stellar masses $\log M_*/M_{\odot}$ = [10.5;11.0] (this is the main mass range of QGs), after entering the cluster, there is a decrease in the radii $R_{90,r}$ by about 30\% when moving towards the center., Comment: 12 pages, 3 figures, 4 tables, accepted: Astrophys. Bull., 01, 2022