Is splitting a real solution? Why can't that powerful group, which had control of the original chain take control of this new fork?
Confused about what you mean by "take control" of the new fork.
The powerful miners are going to download a different set of software with different rules, and mine on it? That would just be supporting the new fork by participating on it, giving it more legitimacy by way of giving it resources (hash power).
*EDIT: You can certainly attack a chain by dedicating your hash power to sabotaging their blocks. This however would make your own chain weaker, and generally not a profitable use of resources.
The answer is that miners would have to take mining power away from the chain that they were mining. In practice the mining power that each chain receives is proportional to its current price.
This is also something all the people upset about the electricity that bitcoin mining takes up need to understand. The electricity is being paid for by the people buying the balances that the miners mine. If people weren't buying the massive miner rewards every 10 minutes, the price of bitcoin would not stay the same and the same electricity usage would not be viable.