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Janko Group
In the area of modern algebra known as group theory, the Janko groups are the four sporadic simple groups '' J1'', '' J2'', '' J3'' and '' J4'' introduced by Zvonimir Janko. Unlike the Mathieu groups, Conway groups, or Fischer groups, the Janko groups do not form a series, and the relation among the four groups is mainly historical rather than mathematical. History Janko constructed the first of these groups, ''J''1, in 1965 and predicted the existence of ''J''2 and ''J''3. In 1976, he suggested the existence of ''J''4. Later, ''J''2, ''J''3 and ''J''4 were all shown to exist. ''J''1 was the first sporadic simple group discovered in nearly a century: until then only the Mathieu groups were known, ''M''11 and ''M''12 having been found in 1861, and ''M''22, ''M''23 and ''M''24 in 1873. The discovery of ''J''1 caused a great "sensation" and "surprise"The group theorist Bertram Huppert said of ''J''1: "There were a very few things that surprised me in my life... There were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
