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A group, in mathematics, is a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and operation must satisfy a few conditions, called group axioms, that are familiar from number systems. The ubiquity of groups in numerous areas—both within and outside mathematics—makes them a central organizational tool in contemporary mathematics. The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Today, group theory is a very active mathematical discipline that studies groups in their own right. Symmetry groups are widely applied in molecular chemistry and various physical disciplines. (more...)

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• ... that the Japanese novel Kanikōsen is one of the best-selling books of 2008, despite being published in 1929?
• ... that Thomas Gold Appleton, the brother-in-law of Henry Wadsworth Longfellow known as "the Boston wit", is reported to have said as he was dying, "It will be a new experience"?
• ... that the Export Control Act of 1940 ceased the exportation of military equipment to pre-WWII Japan which pushed the United States and Japan closer to war?
• ... that On the Green Carpet was the first North Korean film to be invited to the Berlin International Film Festival, where it was screened in 2004?
• ... that The Edgewater, an over-water hotel on Seattle's Central Waterfront, used to advertise that you could "fish from your room"?
• ... that actress Dina Cocea was known in Romania as the "Queen of the Theater" and received the country's highest civil award, the Order of the Star of Romania?
  
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• Barack Obama (pictured) of the Democratic Party becomes the first African American to be elected as President of the United States.
• An airplane crashes amidst rush-hour traffic in Mexico City, killing Mexican Secretary of the Interior Juan Camilo Mouriño and eight others.
• Rupiah Banda of the Movement for Multi-Party Democracy is elected President of Zambia.
• Lewis Hamilton wins the 2008 Formula One Drivers' Championship, beating Felipe Massa by one point.
• Sébastien Loeb of the Citroën team becomes the first driver to win the World Rally Championship for a fifth consecutive time.
• Heavy floods affect Vietnam and southern China, flooding Hanoi and killing at least 100.
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November 5: Guy Fawkes Night in the United Kingdom and some Commonwealth countries

• 1605 – Thomas Knyvet arrested explosives expert Guy Fawkes and foiled Robert Catesby's Gunpowder Plot to destroy the Houses of Parliament in London during the State Opening.
• 1688 – Prince William of Orange landed at Brixham in Devon, on his way to depose his father-in-law King James II (pictured), the last Catholic monarch of England.
• 1838 – The collapse of the Federal Republic of Central America began with Nicaragua seceding from the union.
• 1913 – King Otto of Bavaria was deposed by his cousin, Prince Regent Ludwig, who assumed the title Ludwig III of Bavaria.
• 1917 – St. Tikhon of Moscow was elected Patriarch of Moscow and of the Russian Orthodox Church.

• More events: November 4 – November 5 – November 6

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