Here is a question about this article: This set inherits a group operation (sometimes called coset multiplication, or coset addition) from the original group G: (gN) • (hN) = (gh)N for all g and h in G. This definition is motivated by the idea (itself an instance of general structural considerations outlined above) that the map G → G / N that associates to any element g its coset gN be a group homomorphism, or by general abstract considerations called universal properties. The coset eN = N serves as the identity in this group, and the inverse of gN in the quotient group is (gN)−1 = (g−1)N.e[›]
What is the answer to this question: What group operation is taken by the set from the original group?
****
So... coset multiplication


Here is a question about this article: Banner Armies were organized along ethnic lines, namely Manchu and Mongol, but included non-Manchu bondservants registered under the household of their Manchu masters. The years leading up to the conquest increased the number of Han Chinese under Manchu rule, leading Hong Taiji to create the Eight Han Banners (zh), and around the time of the Qing takeover of Beijing, their numbers rapidly swelled. Han Bannermen held high status and power in the early Qing period, especially immediately after the conquest during Shunzhi and Kangxi's reign where they dominated Governor-Generalships and Governorships across China at the expense of both Manchu Bannermen and Han civilians. Han also numerically dominated the Banners up until the mid 18th century. European visitors in Beijing called them "Tartarized Chinese" or "Tartarified Chinese". It was in Qianlong's reign that the Qianlong Emperor, concerned about maintaining Manchu identity, re-emphasized Manchu ethnicity, ancestry, language, and culture in the Eight Banners and started a mass discharge of Han Bannermen from the Eight Banners, either asking them to voluntarily resign from the Banner rolls or striking their names off. This led to a change from Han majority to a Manchu majority within the Banner system, and previous Han Bannermen garrisons in southern China such as at Fuzhou, Zhenjiang, Guangzhou, were replaced by Manchu Bannermen in the purge, which started in 1754. The turnover by Qianlong most heavily impacted Han banner garrisons stationed in the provinces while it less impacted Han Bannermen in Beijing, leaving a larger proportion of remaining Han Bannermen in Beijing than the provinces. Han Bannermen's status was decreased from that point on with Manchu Banners gaining higher status. Han Bannermen numbered 75% in 1648 Shunzhi's reign, 72% in 1723 Yongzheng's reign, but decreased to 43% in 1796 during the first year of Jiaqing's reign, which was after Qianlong's purge. The mass discharge was known as the Disbandment of the Han Banners (zh). Qianlong directed most of his ire at those Han Bannermen descended from defectors who joined the Qing after the Qing passed through the Great Wall at Shanhai Pass in 1644, deeming their ancestors as traitors to the Ming and therefore untrustworthy, while retaining Han Bannermen who were descended from defectors who joined the Qing before 1644 in Liaodong and marched through Shanhai pass, also known as those who "followed the Dragon through the pass" (從龍入關; cong long ru guan).
What is the answer to this question: When did Manchu ethnicity become important again in the Eight Banners?
****
So... Qianlong's reign


Here is a question about this article: Her fourth studio album 4 was released on June 28, 2011 in the US. 4 sold 310,000 copies in its first week and debuted atop the Billboard 200 chart, giving Beyoncé her fourth consecutive number-one album in the US. The album was preceded by two of its singles "Run the World (Girls)" and "Best Thing I Never Had", which both attained moderate success. The fourth single "Love on Top" was a commercial success in the US. 4 also produced four other singles; "Party", "Countdown", "I Care" and "End of Time". "Eat, Play, Love", a cover story written by Beyoncé for Essence that detailed her 2010 career break, won her a writing award from the New York Association of Black Journalists. In late 2011, she took the stage at New York's Roseland Ballroom for four nights of special performances: the 4 Intimate Nights with Beyoncé concerts saw the performance of her 4 album to a standing room only.
What is the answer to this question: Beyonce's fourth album debuted in what year?
****
So...
2011