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şehir merkezi: town/city center
şehrin merkezi: center of town/city

No.

grub|u, merkez|i are marked with a (technically 3rd person) possessive suffix. It ties these compounds together as one unit:

                              müzik grubu

                              şehir merkezi

Sometimes the first part takes nominative sometimes genitive but that is another story. You can find many articles on that issue.

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