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Held Group
In the area of modern algebra known as group theory, the Held group ''He'' is a sporadic simple group of Order (group theory), order : 21033527317 = 4030387200 : ≈ 4. History ''He'' is one of the 26 sporadic groups and was found by during an investigation of simple groups containing an involution whose centralizer is isomorphic to that of an involution in the Mathieu group M24, Mathieu group M24. A second such group is the projective linear group, linear group L5(2). The Held group is the third possibility, and its construction was completed by John McKay (mathematician), John McKay and Graham Higman. The outer automorphism group has order 2 and the Schur multiplier is trivial. Representations The smallest faithful complex representation has dimension 51; there are two such representations that are duals of each other. It centralizer, centralizes an element of order 7 in the Monster group. As a result the prime 7 plays a special role in the theory of ... [...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] |
