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Two groups G and H are called isomorphic if there exist group homomorphisms a: G → H and b: H → G, such that applying the two functions one after another in each of the two possible orders gives the identity functions of G and H. That is, a(b(h)) = h and b(a(g)) = g for any g in G and h in H. From an abstract point of view, isomorphic groups carry the same information. For example, proving that g • g = 1G for some element g of G is equivalent to proving that a(g) ∗ a(g) = 1H, because applying a to the first equality yields the second, and applying b to the second gives back the first.
What are two groups called if they include homomorphisms?
A: isomorphic

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Napoleon instituted lasting reforms, including higher education, a tax code, road and sewer systems, and established the Banque de France, the first central bank in French history. He negotiated the Concordat of 1801 with the Catholic Church, which sought to reconcile the mostly Catholic population to his regime. It was presented alongside the Organic Articles, which regulated public worship in France. His dissolution of the Holy Roman Empire paved the way to German Unification later in the 19th century. The sale of the Louisiana Territory to the United States doubled the size of the country and was a major event in American history.
What is the name of the empire Napoleon dissolved that later led to unification in Germany?
A: the Holy Roman Empire

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The city also had a large class of free people of color. By 1860, 3,785 free people of color were in Charleston, nearly 18% of the city's black population, and 8% of the total population. Free people of color were far more likely to be of mixed racial background than slaves. Many were educated, practiced skilled crafts, and some even owned substantial property, including slaves. In 1790, they established the Brown Fellowship Society for mutual aid, initially as a burial society. It continued until 1945.
In what year did the Brown Fellowship Society start?
A: unanswerable

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Typically the sub-Tropical High Pressure Belt, with frequent clear skies, provides more than 300 days of sunshine per year. It is situated at the southern edge of the tropics; the Tropic of Capricorn cuts the country about in half. The winter (June – August) is generally dry, both rainy seasons occur in summer, the small rainy season between September and November, the big one between February and April. Humidity is low, and average rainfall varies from almost zero in the coastal desert to more than 600 mm in the Caprivi Strip. Rainfall is however highly variable, and droughts are common. The last[update] bad rainy season with rainfall far below the annual average occurred in summer 2006/07.
How much rain typically falls in February each year in the Caprivi Strip?
A:
unanswerable