How do I convince the management that this training is very important
from the QA perspective as this is the team that will find bugs and
which will reduce the maintenance cost?
I'd suggest taking the approach of asking how much of a cost will be incurred by QA and development having to spend time to build up QA's expertise in this tool that could be reduced by the training. QA has to know how the tool will be used which if done in a trial and error fashion could be rather expensive if there is a lot of time spent tracking down answers about how something could be used.
Something to consider though is what is the cost to the company in having QA do the training? If the training is done on the company time and the average QA person is being paid $15/hour, given an 8 hour work day and the training is 2 days that cost is $2400 just to pay the employees. Add the cost of the training and possible transportation costs if the training is done off-site and you have to show how this is a good investment for the company to make. Why is doing this such a good idea? Well, the expertise QA could gain would make the testing be more efficient and effective resulting in a higher quality product initially.