The common denominator here is human greed and lack of regulations protecting everybody else. Authoritarianism is a feature of that, regardless of what system you're talking about. Economic policy has little bearing on whether or not a one party system turns into a dictatorship. A capitalist country in the same position would end up the same way, although more likely it would become a corporatocracy. There have been a handful of successful communist societies (largely on the small scale, like those boats that were stranded in a canal who formed their own communal society for a number of years because the companies that owned the boats didn't care enough to bother rescuing them), but the issues of both communism and capitalism always come back to simple everyday human greed and too much power in too few hands.

The modern Russian oligarchs made their fortune when Russia, the Ukraine, and one other country I can't remember joined together to dissolve the USSR in order to destabilize the economy so they could enact a stock market and buy up all the previously government owned industries before anyone else could. They even flew American stock market experts over beforehand to teach them how to do it. Given the opportunity, they would've done the exact same thing in a capitalist country. I'm not here to defend the USSR, because it absolutely had plenty of problems (authoritarianism among them), but those pictures from the 90s of people starving in the streets are from that period where Russia transitioned from a planned economy to a more capitalist economy.