Steinberg-like characters for finite simple groups
نویسندگان
چکیده
منابع مشابه
Characters of Finite Abelian Groups
Example 1.2. The trivial character of G is the homomorphism 1G defined by 1G(g) = 1 for all g ∈ G. Example 1.3. Let G be cyclic of order 4 with generator γ. Since γ4 = 1, a character χ of G has χ(γ)4 = 1, so χ takes only four possible values at γ, namely 1, −1, i, or −i. Once χ(γ) is known, the value of χ elsewhere is determined by multiplicativity: χ(γj) = χ(γ)j . So we get four characters, wh...
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When G has size n and g ∈ G, for any character χ of G we have χ(g)n = χ(gn) = χ(1) = 1, so the values of χ lie among the nth roots of unity in S1. More precisely, the order of χ(g) divides the order of g (which divides #G). Characters on finite abelian groups were first studied in number theory, since number theory is a source of many interesting finite abelian groups. For instance, Dirichlet u...
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In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2019
ISSN: 1435-4446,1433-5883
DOI: 10.1515/jgth-2019-0024