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- W25646722 abstract "This chapter reviews finite projective groups. One of the oldest problems in finite group theory is that of finding the complex finite projective groups of a given degree n, i.e., the finite subgroups L of PGL(n, C). For small n, the finite projective groups L of degree n have been determined. For the most interesting of these, the factor group L/Z(L) of L modulo its center Z(L) are simple. This leads to the question: To what extent can the problem of finding all finite subgroups L of PGL(n, K) be reduced to the special case where L/Z(L) is simple? Huppert devised a technique using which problems of this kind can be approached. The technique can be defined as a two part definition: (1) an irreducible subgroup L of GL(n, K) is strongly irreducible, if every normal subgroup N not contained in Z(L) is irreducible; and, (2) a subgroup L of GL(n, q) is quasi-primitive, if it is irreducible, and if in any normal subgroup N of L, any two irreducible constituents are similar." @default.
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- W25646722 date "1977-01-01" @default.
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- W25646722 title "On finite projective groups" @default.
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- W25646722 doi "https://doi.org/10.1016/b978-0-12-080550-1.50010-x" @default.
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