In Manifest we require only the following things to show google map:
<manifest ….>
<uses-permission android:name="android.permission.INTERNET" />
<uses-permission android:name="android.permission.ACCESS_NETWORK_STATE" />
<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
<uses-permission android:name="com.google.android.providers.gsf.permission.READ_GSERVICES" />
<application ….>
<activity … />
<meta-data android:name="com.google.android.gms.version" android:value="@integer/google_play_services_version" />
<meta-data android:name="com.google.android.maps.v2.API_KEY" android:value="your api key" />
</application>
<uses-feature android:glEsVersion="0x00020000" android:required="true" />
</manifest>
Change your fragment tag as:
<fragment
android:id="@+id/map"
android:layout_width="match_parent"
android:layout_height="match_parent"
class="com.google.android.gms.maps.SupportMapFragment"/>
Clean your project and run.