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Any element generates its own cyclic subgroup, such as z 2 = { e, z 2, z 4} of order 3, isomorphic to C 3 and Z/3Z; and z 5 = { e, z 5, z 10 = z 4, z 15 = z 3, z 20 = z 2, z 25 = z} = G, so that z 5 has order 6 and is an alternative generator of G.
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
NP-complete problems are in NP, the set of all decision problems whose solutions can be verified in polynomial time; NP may be equivalently defined as the set of decision problems that can be solved in polynomial time on a non-deterministic Turing machine.
The earlier term for the discipline was "political economy", but since the late 19th century, it has commonly been called "economics". [22] The term is ultimately derived from Ancient Greek οἰκονομία (oikonomia) which is a term for the "way (nomos) to run a household (oikos)", or in other words the know-how of an οἰκονομικός (oikonomikos), or "household or homestead manager".
[5] [6] [7] The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical. [ 4 ] [ 8 ] [ 9 ] The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon ( c. 570 – c. 478 BC), who had been one of his contemporaries.
Ronald Wilson Reagan [a] (February 6, 1911 – June 5, 2004) was an American politician and actor who served as the 40th president of the United States from 1981 to 1989. He was a member of the Republican Party and became an important figure in the American conservative movement.
According to the 2011 census, there were 10.1 million child labourers in the country, a decline of 2.6 million from 12.6 million in 2001. [ 354 ] Since 1991, economic inequality between India's states has consistently grown: the per-capita net state domestic product of the richest states in 2007 was 3.2 times that of the poorest. [ 355 ]
Ex-USS Eberle; Hunt-class destroyers Adrias (D06) (1946–1963) – The ex-HMS Tanatside was acquired on loan as a replacement for the first Adrias (L67). She was returned to the Royal Navy in 1963. [4] Adrias (L67) (1942–1945) – The ex-HMS Border was seriously damaged by mines on October 22, 1943. Although the ship survived, it was not ...