Products of characters and finite p -groups II
نویسندگان
چکیده
منابع مشابه
Some Observations on Products of Characters of Finite Classical Groups
This is an extended version of the talk given by the first author at the conference. We report on the outcome of some experiments with the decomposition of products of (generalized) characters of some classical groups. In particular some results of the PhD-thesis of Dirk Mattig on the products of unipotent characters of general linear groups are presented and commented. In order to obtain simil...
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The proof of this theorem is based on the correspondence between the characters of a uniform pro-p group and the orbits of the action of the group on the dual of its Lie algebra. This result is an analogue of the Kirillov theory, introduced first in the context of nilpotent Lie groups and then used in many other situations (see [7]). The correspondence is quite explicit and it also gives the ex...
متن کاملCharacters 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...
متن کاملMonomial Characters of Finite Groups
An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters — those induced from a linear character of some subgroup — since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the cl...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2004
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-003-4825-7