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Thin Finite Groups
In the mathematical classification of finite simple groups, a thin group is a finite group such that for every odd prime number ''p'', the Sylow ''p''-subgroups of the 2- local subgroups are cyclic. Informally, these are the groups that resemble rank 1 groups of Lie type over a finite field of characteristic 2. defined thin groups and classified those of characteristic 2 type in which all 2-local subgroups are solvable. The thin simple groups were classified by . The list of finite simple thin groups consists of: *The projective special linear groups PSL2(''q'') and PSL3(''p'') for ''p'' = 1 + 2''a''3''b'' and PSL3(4) *The projective special unitary groups PSU3(''p'') for ''p'' =−1 + 2''a''3''b'' and ''b'' = 0 or 1 and PSU3(2''n'') *The Suzuki groups Sz(2''n'') *The Tits group 2''F''4(2)' *The Steinberg group 3''D''4(2) *The Mathieu group ''M''11 *The Janko group J1 See also *Quasithin group References * * *{{Citation , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classification Of Finite Simple Groups
In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic. The proof consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004. Simple groups can be seen as the basic building blocks of all finite groups, reminiscent of the way the prime numbers are the basic building blocks of the natural numbers. The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference from integer factorization is that such "building blocks" do not necessarily determine a unique group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extension prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
