Some Tajiks would like to see their own man, Mohammed Fahim, make a bid for power.
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The United Nations reckons that about eight out of ten Tajiks live in poverty.
It is an ethnic hodge-podge of Uzbeks and Tajiks, Aimaq and Hazaras, Turkmen, Mongols and Baluch.
For example, Sokh, an enclave administered by Uzbekistan, is in Kirgizstan but its people are Tajiks.
Both these measures will, by the same token, damage Mr Karzai's relations with the Northern Alliance's warlords, who are mainly Tajiks and Uzbeks.
ECONOMIST: The face of the new Afghanistan starts to take shape
Nine Tajiks, said to have been living in a caravan, died in a fire in the Moscow region last week.
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Tajiks speak Persian, whereas Azeris, Turkmen, Uzbeks and Kazakhs speak Turkic languages.
Three senior jobs will be taken by prominent Tajiks associated with the legendary Tajik commander, Ahmad Shah Masood, who was killed in September.
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One country the Tajiks would like to see become more involved is Russia, still Tajikistan's principal strategic partner despite America's increased presence in Central Asia.
Tajiks form the second largest group, followed by Uzbeks and Hazaras.
Karzai, in his efforts to mollify his restive fellow-Pashtuns, has made conciliatory gestures to the Taliban which have alienated Tajiks and Uzbeks who helped him come to power.
Tajiks, however, retained their influence, keeping the ministries of defence and foreign affairs, while the former king, a Pushtun, came under pressure to withdraw from the presidential race.
In Afghanistan, what we called the Northern Alliance was an alliance of Sunni Tajiks, Sunni Uzbeks and Shiite Hazaras, and so they jointly took over Kabul together in 2001.
It says it can no longer supply gas to the Tajiks as it has to meet growing demand from its main partner, China, but the amount Tajikistan needs is small by comparison.
Arms sent to the Nuri group from Tajiks in north-east Afghanistan were countered by supplies from Russia and Tajikistan's neighbour Uzbekistan, both determined to stop Islamists gaining power close to their territory.
It rose little by little on the horizon line as we power walked our way to it, passed the Kazakhs and Tajiks selling trinkets and wrestling with each other in the square.
It is a compromise between the claims of the Pushtuns (the country's largest ethnic group, to which both Mr Karzai and most of the Taliban belong) and the Northern Alliance of minority Tajiks and Uzbeks.
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Another reason for American caution is that the usefulness as a fighting force of the Northern Alliance's mixture of Tajiks, Uzbeks and others, though greater than many sceptics had believed two months ago, may now be drawing to an end.
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Even after the Arab conquest, Persian remained the language of local rulers, as Iranian administrators, mullahs and traders settled in the cities of Transoxania (which covered much of today's Uzbekistan, Turkmenistan and Tajikistan), and is the basis of the language spoken by the Tajiks today.
Olivier Roy, a Paris-based specialist on Central Asia, points to the cultural split in the region between the nomads from the steppes and mountains, mainly Kirgizs, Kazakhs and Turkmens, and the sedentary, mainly urban Uzbeks and Tajiks who settled in the river basins of Transoxania.
Katta Ashula (literally big song ) is a type of traditional song that forms part of the identity of various peoples of the Ferghana Valley in Uzbekistan, which is also home to Tajiks, Uyghurs and Turks, and of some regions of Kyrgyzstan, Tajikistan and Kazakhstan.
But I then traveled up to the Panjshir Valley, north of Kabul, a largely Tajik area, and there people were voting in significant numbers, not least because the Tajiks are a minority, want to, try to acquire a block of power in parliament to counterbalance what they say is a Pashtun-governated Karzai administration in Afghanistan.
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