Problem: 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?
The answer is the following: isomorphic

Problem: Shell sold 9.5% of its 23.1% stake in Woodside Petroleum in June 2014 and advised that it had reached an agreement for Woodside to buy back 9.5% of its shares at a later stage. Shell became a major shareholder in Woodside after a 2001 takeover attempt was blocked by then federal Treasurer Peter Costello and the corporation has been open about its intention to sell its stake in Woodside as part of its target to shed assets. At a general body meeting, held on 1 August 2014, 72 percent of shareholders voted to approve the buy-back, short of the 75 percent vote that was required for approval. A statement from Shell read: "Royal Dutch Shell acknowledges the outcome of Woodside Petroleum Limited's shareholders' negative vote on the selective buy-back proposal. Shell is reviewing its options in relation to its remaining 13.6 percent holding."
Who blocked the takeover attempt?
The answer is the following: then federal Treasurer Peter Costello

Problem: Along with dividing up their project by theoretical emphasis, anthropologists typically divide the world up into relevant time periods and geographic regions. Human time on Earth is divided up into relevant cultural traditions based on material, such as the Paleolithic and the Neolithic, of particular use in archaeology.[citation needed] Further cultural subdivisions according to tool types, such as Olduwan or Mousterian or Levalloisian help archaeologists and other anthropologists in understanding major trends in the human past.[citation needed] Anthropologists and geographers share approaches to Culture regions as well, since mapping cultures is central to both sciences. By making comparisons across cultural traditions (time-based) and cultural regions (space-based), anthropologists have developed various kinds of comparative method, a central part of their science.
How do anthropologists typically like to divide up the world?
The answer is the following: relevant time periods and geographic regions

Problem: Most of the fairs and festivals in Kathmandu originated in the Malla period or earlier. Traditionally, these festivals were celebrated by Newars. In recent years, these festivals have found wider participation from other Kathmanduites as well. As the capital of the Republic of Nepal, various national festivals are celebrated in Kathmandu. With mass migration to the city, the cultures of Khas from the west, Kirats from the east, Bon/Tibetan from the north, and Mithila from the south meet in the capital and mingle harmoniously. The festivities such as the Ghode (horse) Jatra, Indra Jatra, Dashain Durga Puja festivals, Shivratri and many more are observed by all Hindu and Buddhist communities of Kathmandu with devotional fervor and enthusiasm. Social regulation in the codes enacted incorporate Hindu traditions and ethics. These were followed by the Shah kings and previous kings, as devout Hindus and protectors of Buddhist religion.
In relation to Kathmandu, where do the Tibetans hale?
The answer is the following:
north