High Quality Content by WIKIPEDIA articles! In the mathematical subject of group theory, the Grushko theorem or the Grushko-Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality of a generating set) of a free product of two groups is equal to the sum of the ranks of the two free factors. The theorem was first obtained in a 1940 article of Grushko and then, independently, in a 1943 article of Neumann. After the original proofs of Grushko (1940) and Neumann(1943),...
High Quality Content by WIKIPEDIA articles! In the mathematical subject of group theory, the Grushko theorem or the Grushko-Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality of a generating set) of a free product of two groups is equal to the sum of the ranks of the two free factors. The theorem was first obtained in a 1940 article of Grushko and then, independently, in a 1943 article of Neumann. After the original proofs of Grushko (1940) and Neumann(1943), there were many subsequent alternative proofs, simplifications and generalizations of Grushko's theorem. A close version of Grushko's original proof is given in the 1955 book of Kurosh. Like the original proofs, Lyndon's proof (1965) relied on length-functions considerations but with substantial simplifications. A 1965 paper of Stallings gave a greatly simplified topological proof of Grushko's theorem.
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Шесть кроликов гуляли по краешку земли, огромную морковку шесть кроликов нашли. Может быть, сделать из нее дом? Или корабль? А что если это морковка-самолет? Что кролики сделали с этим невиданным чудом - узнаем, прочитав книжку. Эту веселую историю придумала художница Сатое Тоне. Она родилась в Японии, в последние годы живет и работает в Италии. В 2013 году художница стала лауреатом Международной...
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