Question: Sub- and quotient groups are related in the following way: a subset H of G can be seen as an injective map H G, i.e. any element of the target has at most one element that maps to it. The counterpart to injective maps are surjective maps (every element of the target is mapped onto), such as the canonical map G G / N.y["] Interpreting subgroup and quotients in light of these homomorphisms emphasizes the structural concept inherent to these definitions alluded to in the introduction. In general, homomorphisms are neither injective nor surjective. Kernel and image of group homomorphisms and the first isomorphism theorem address this phenomenon.
Try to answer this question if possible: What theory address the phenomenon of homomorphisms being neither injective nor surjective?
Answer: the first isomorphism theorem
Question: The pagan Slavic populations were Christianized between the 6th and 10th centuries. Orthodox Christianity is predominant in the East and South Slavs, while Roman Catholicism is predominant in West Slavs and the western South Slavs. The religious borders are largely comparable to the EastWest Schism which began in the 11th century. The majority of contemporary Slavic populations who profess a religion are Orthodox, followed by Catholic, while a small minority are Protestant. There are minor Slavic Muslim groups. Religious delineations by nationality can be very sharp; usually in the Slavic ethnic groups the vast majority of religious people share the same religion. Some Slavs are atheist or agnostic: only 19% of Czechs professed belief in god/s in the 2005 Eurobarometer survey.
Try to answer this question if possible: Most of what populations are Muslim?
Answer: unanswerable
Question: When not dressed in Westernized clothing such as jeans and t-shirts, Somali men typically wear the macawis, which is a sarong-like garment worn around the waist. On their heads, they often wrap a colorful turban or wear the koofiyad, an embroidered fez.
Try to answer this question if possible: Where is the macawis worn?
Answer: around the waist
Question: The Marxist critique of capitalism developed with Friedrich Engels was, alongside liberalism and fascism, one of the defining ideological movements of the Twentieth Century. The industrial revolution produced a parallel revolution in political thought. Urbanization and capitalism greatly reshaped society. During this same period, the socialist movement began to form. In the mid-19th century, Marxism was developed, and socialism in general gained increasing popular support, mostly from the urban working class. Without breaking entirely from the past, Marx established principles that would be used by future revolutionaries of the 20th century namely Vladimir Lenin, Mao Zedong, Ho Chi Minh, and Fidel Castro. Though Hegel's philosophy of history is similar to Immanuel Kant's, and Karl Marx's theory of revolution towards the common good is partly based on Kant's view of historyMarx declared that he was turning Hegel's dialectic, which was "standing on its head", "the right side up again". Unlike Marx who believed in historical materialism, Hegel believed in the Phenomenology of Spirit. By the late 19th century, socialism and trade unions were established members of the political landscape. In addition, the various branches of anarchism, with thinkers such as Mikhail Bakunin, Pierre-Joseph Proudhon or Peter Kropotkin, and syndicalism also gained some prominence. In the Anglo-American world, anti-imperialism and pluralism began gaining currency at the turn of the 20th century.
Try to answer this question if possible: Whose theory of revolution is similar to Immanuel Kant's philosophy of history?
Answer:
unanswerable