I have a tablet Samsung Galaxy Tab 10.1 (P7500) with stock firmware P7500XWLPG (Android 4.0.4). I want to install Chrome Browser on it. But when I find it in Google Play I see message "This app is incompatible with your device". Is it any way to solve this problem and install Chrome on my tablet?
It is very much possible that support for API level 15 or below has been dropped for all the current Chrome builds of version 47.0.2526.83 or perhaps it has been so for the last few versions as well. I updated my Chrome app in Jelly Bean 4.2.1 and I can see that the minimum API level it requires is 16 and is targeted at 23.
Android versions corresponding to API level 16 are Android 4.1 and 4.1.1 while Android 4.0.4 has API level 15. Clearly, your Android version is not compatible with latest Chrome build.
Considering the details, I suggest you now move on to a different browser. That said, you can still use Chrome browser at a huge price. You can download an older build of Chrome which is compatible with your Android version (read API level), from a trustworthy source . The price you'll be paying is risking your device with infection from online malwares, simply because outdated as well as popular software is a goldmine for malware writers.
For your information, I've the APK of Chrome v39.xx and I can see that the minimum API level it requires is 14 and not 16.