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Rudvalis Group
In the area of modern algebra known as group theory, the Rudvalis group ''Ru'' is a sporadic simple group of order : 214335371329 : = 145926144000 : ≈ 1. History ''Ru'' is one of the 26 sporadic groups and was found by and constructed by . Its Schur multiplier has order 2, and its outer automorphism group is trivial. In 1982 Robert Griess showed that ''Ru'' cannot be a subquotient of the monster group.Griess (1982) Thus it is one of the 6 sporadic groups called the pariahs. Properties The Rudvalis group acts as a rank 3 permutation group on 4060 points, with one point stabilizer being the Ree group 2''F''4(2), the automorphism group of the Tits group. This representation implies a strongly regular graph srg(4060, 2304, 1328, 1208). That is, each vertex has 2304 neighbors and 1755 non-neighbors, any two adjacent vertices have 1328 common neighbors, while any two non-adjacent ones have 1208 . Its double cover acts on a 28-dimensional lattice over the ... [...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] |
