Connection between the Hazara people and the Khazars?

HPIN: We have created a community page on Facebook to collect information about any possible relationship between the Hazaras and the Khazars.
Both peoples are Turkic and some Turkic historians in Afghanistan strongly believe in direct connection between them. They say the name of the Khazar sea (Caspian) and Hazar city of Turkmenistan have been taken from the Hazara or the Khazar people.

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