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The modern concept of an abstract group developed out of several fields of mathematics. The original motivation for group theory was the quest for solutions of polynomial equations of degree higher than 4. The 19th-century French mathematician Evariste Galois, extending prior work of Paolo Ruffini and Joseph-Louis Lagrange, gave a criterion for the solvability of a particular polynomial equation in terms of the symmetry group of its roots (solutions). The elements of such a Galois group correspond to certain permutations of the roots. At first, Galois' ideas were rejected by his contemporaries, and published only posthumously. More general permutation groups were investigated in particular by Augustin Louis Cauchy. Arthur Cayley's On the theory of groups, as depending on the symbolic equation n = 1 (1854) gives the first abstract definition of a finite group.
Who developed a theory giving the first abstract definition of a finite group?
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The answer: Arthur Cayley

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By the mid-18th century, the Qing had successfully put outer regions such as Inner and Outer Mongolia, Tibet and Xinjiang under its control. Imperial commissioners and garrisons were sent to Mongolia and Tibet to oversee their affairs. These territories were also under supervision of a central government institution called Lifan Yuan. Qinghai was also put under direct control of the Qing court. Xinjiang, also known as Chinese Turkestan, was subdivided into the regions north and south of the Tian Shan mountains, also known today as Dzungaria and Tarim Basin respectively, but the post of Ili General was established in 1762 to exercise unified military and administrative jurisdiction over both regions. Dzungaria was fully opened to Han migration by the Qianlong Emperor from the beginning. Han migrants were at first forbidden from permanently settling in the Tarim Basin but were the ban was lifted after the invasion by Jahangir Khoja in the 1820s. Likewise, Manchuria was also governed by military generals until its division into provinces, though some areas of Xinjiang and Northeast China were lost to the Russian Empire in the mid-19th century. Manchuria was originally separated from China proper by the Inner Willow Palisade, a ditch and embankment planted with willows intended to restrict the movement of the Han Chinese, as the area was off-limits to civilian Han Chinese until the government started colonizing the area, especially since the 1860s.
When did Tibet become part of Qing China?
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The answer: mid-18th century

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Another source of loanwords was Old Norse, which came into contact with Old English via the Scandinavian rulers and settlers in the Danelaw from the late 9th century, and during the rule of Cnut and other Danish kings in the early 11th century. Many place-names in eastern and northern England are of Scandinavian origin. Norse borrowings are relatively rare in Old English literature, being mostly terms relating to government and administration. The literary standard, however, was based on the West Saxon dialect, away from the main area of Scandinavian influence; the impact of Norse may have been greater in the eastern and northern dialects. Certainly in Middle English texts, which are more often based on eastern dialects, a strong Norse influence becomes apparent. Modern English contains a great many, often everyday, words that were borrowed from Old Norse, and the grammatical simplification that occurred after the Old English period is also often attributed to Norse influence.
What language was a source for English loanwords that are still used today?
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The answer: Old Norse

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In 2013, Washington University received a record 30,117 applications for a freshman class of 1,500 with an acceptance rate of 13.7%. More than 90% of incoming freshmen whose high schools ranked were ranked in the top 10% of their high school classes. In 2006, the university ranked fourth overall and second among private universities in the number of enrolled National Merit Scholar freshmen, according to the National Merit Scholar Corporation's annual report. In 2008, Washington University was ranked #1 for quality of life according to The Princeton Review, among other top rankings. In addition, the Olin Business School's undergraduate program is among the top 4 in the country. The Olin Business School's undergraduate program is also among the country's most competitive, admitting only 14% of applicants in 2007 and ranking #1 in SAT scores with an average composite of 1492 M+CR according to BusinessWeek.
What percentage of incoming freshman at Washington University were in the top %10 of their class in 2013?
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The answer:
More than 90% of incoming freshmen