ZP

ZP may refer to:

Multiplicative group of integers modulo n

In modular arithmetic the set of congruence classes relatively prime to the modulus number, say n, form a group under multiplication called the multiplicative group of integers modulo n. It is also called the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. (Units refers to elements with a multiplicative inverse.)

This group is fundamental in number theory. It has found applications in cryptography, integer factorization, and primality testing. For example, by finding the order of this group, one can determine whether n is prime: n is prime if and only if the order is n − 1.

Group axioms

It is a straightforward exercise to show that, under multiplication, the set of congruence classes modulo n that are relatively prime to n satisfy the axioms for an abelian group.

Because a ≡ b (mod n) implies that gcd(a, n) = gcd(b, n), the notion of congruence classes modulo n that are relatively prime to n is well-defined.

Procter & Gamble

Procter & Gamble Co., also known as P&G, is an American multinational consumer goods company headquartered in downtown Cincinnati, Ohio, United States, founded by William Procter and James Gamble, both from the United Kingdom. Its products include cleaning agents, and personal care products. Prior to the sale of Pringles to the Kellogg Company, its product line included foods and beverages. In 2014, P&G recorded $83.1 billion in sales. On August 1, 2014, P&G announced it was streamlining the company, dropping around 100 brands and concentrating on the remaining 80 brands, which produced 95 percent of the company's profits. A.G. Lafley, the company's chairman, president and CEO until October 31, 2015, said the future P&G would be "a much simpler, much less complex company of leading brands that's easier to manage and operate". David Taylor became P&G CEO and President effective November 1, 2015. P&G remains a highly selective employer as less than 1% of all applicants are hired annually.

PG

PG or P.G. may refer to:

Business and products

Companies and organizations

People

Paul Garmirian (cigar brand)

Paul Garmirian, or P.G, is a noted cigar brand named after its founder, Lebanese born cigar connoisseur Paul Garmirian.

History

Paul Garmirian founded his company in 1990 after doing extensive research on cigars for his book The Gourmet Guide to Cigars, published the same year. Paul Garmirian separates himself from other cigar manufacturers because he does not sell to discount catalogs or wholesalers. He sticks true to his word and limits the number of shops that can carry his product.

Notable smokers

Paul Garmirian cigars are famous for being a choice cigar for Washington insiders. According to US News & World Report,Presidents Bill Clinton, George H.W. Bush, and George W. Bush all have indulged in PGs. Candidates who ran for US President in the 2008 Presidential Race, Republican Party candidate Rudy Giuliani and Democratic Party candidate Bill Richardson have been known to enjoy Paul Garmirian cigars. Other politicians that enjoy Paul Garmirian cigars include California governor Arnold Schwarzenegger, former Tennessee Senator and Law & Order star Fred Thompson, and former Central Intelligence Agency director George Tenet. David Letterman is also known to smoke PG cigars.

Z.P.G.

Z.P.G. (short for "Zero Population Growth") is a 1972 Danish-American dystopian science fiction film starring Oliver Reed and Geraldine Chaplin and directed by Michael Campus. It is inspired by the non-fiction best-selling book The Population Bomb by Paul R. Ehrlich. The film concerns an overpopulated, very polluted future Earth, whose world government executes those who violate a 30-year ban on having children. Filmed in Denmark, the film is almost entirely set-bound featuring art direction designed to reflect a bleak, oppressive future.

Plot

Set in the future, the Earth has become severely polluted (people need to wear breathing masks when outside) with severe overpopulation affecting available resources. Because of the permanent thick smog that has settled over the dismal cities that now cover the Earth’s entire surface, all animals – even common household pets - are extinct; people eat tasteless bright-colored paste out of plastic containers. To reduce the world's population, the world's government decrees that no children may be conceived for the next 30 years. Breaking this law will result in a death penalty for both the parents as well as the newborn. Brainwashing and robot substitutes are used to end the yearning for children with the death penalty as the ultimate deterrent, by being placed under a plastic dome and suffocated to death. Couples of child-bearing age visit "Babyland" and are given life-size animatronic children instead.