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Order (group Theory)
In mathematics, the order of a finite group is the number of its elements. If a group (mathematics), group is not finite, one says that its order is ''infinite''. The ''order'' of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplicative group, multiplication, the order of an element of a group, is thus the smallest positive integer such that , where denotes the identity element of the group, and denotes the product of copies of . If no such exists, the order of is infinite. The order of a group is denoted by or , and the order of an element is denoted by or , instead of \operatorname(\langle a\rangle), where the brackets denote the generated group. Lagrange's theorem (group theory), Lagrange's theorem states that for any subgroup of a finite group , the order of the subgroup divides the order of the group; that is, is a divisor of . In particular, the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Powers Of Rotation, Shear, And Their Compositions
Powers may refer to: Arts and media * Powers (comics), ''Powers'' (comics), a comic book series by Brian Michael Bendis and Michael Avon Oeming ** Powers (American TV series), ''Powers'' (American TV series), a 2015–2016 series based on the comics * Powers (British TV series), ''Powers'' (British TV series), a 2004 children's science-fiction series * Powers (duo), an American pop group * Powers (novel), ''Powers'' (novel), an ''Annals of the Western Shore'' novel by Ursula K. Le Guin * ''Powers: A Study in Metaphysics'', a 2003 book by George Molnar * ''Powers'', a 2019 album by the Futureheads Businesses and organizations * Powers (whiskey), a brand of Irish whiskey * Powers Dry Goods, an American department store chain * Powers Motion Picture Company, an American film company * Powers Motorsports, an American racing team Places in the United States Cities and communities * Powers, Indiana * Powers, Michigan * Powers, Oregon * Powers Coal Camp, Kentucky * Powers Lake, North D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |