A group is a mathematical set of elements 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, namely associativity, identity and invertibility. The ubiquity of groups in numerous areas—both within and outside mathematics—makes them a central organizing principle of 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. Modern group theory—a very active mathematical discipline—studies groups in their own right. To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups.
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_________________________ Today's selected anniversaries:
1605:
The Gunpowder Plot: Thomas Knyvet arrested explosives expert Guy Fawkes and foiled Robert Catesby's plot to destroy the Houses of Parliament in London during the State Opening. (http://en.wikipedia.org/wiki/Gunpowder_Plot)
1688:
Glorious Revolution: Protestant Prince William of Orange landed at Brixham in Devon, on his way to depose his father-in-law King James II, the last Catholic monarch of England. (http://en.wikipedia.org/wiki/Glorious_Revolution)
1838:
The collapse of the Federal Republic of Central America began with Nicaragua seceding from the union. (http://en.wikipedia.org/wiki/Federal_Republic_of_Central_America)
1872:
American Suffragette Susan B. Anthony voted in the U.S. presidential election for the first time in Rochester, New York. She was later fined US$100 for her participation, which she never paid, and the government never pursued her for nonpayment. (http://en.wikipedia.org/wiki/Susan_B._Anthony)
1917:
St. Tikhon of Moscow was elected Patriarch of Moscow and of the Russian Orthodox Church. (http://en.wikipedia.org/wiki/Tikhon_of_Moscow)
_______________________ Wiktionary's word of the day:
autochthonous (adj) 1. Native to the place where found; indigenous. 2. (geology) Buried in place, especially of a fossil preserved in its life position without disturbance or disarticulation. (http://en.wiktionary.org/wiki/autochthonous)
______________________ Wikiquote quote of the day:
War may sometimes be a necessary evil. But no matter how necessary, it is always an evil, never a good. We will not learn how to live together in peace by killing each other's children. --Jimmy Carter (http://en.wikiquote.org/wiki/Jimmy_Carter)