Characters and cohomology of finite 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...
متن کاملCharacters of Finite Abelian Groups
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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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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Let G be a finite group, F an algebraically closed field of finite characteristic p, and let B be a block of FG. We show that the Hochschild and Linckelmann cohomology rings of B are isomorphic, modulo their radicals, in the cases where (1) B is cyclic and (2) B is arbitrary and G either a nilpotent group or a Frobenius group (p odd). (The second case is a consequence of a more general result)....
متن کاملExponents and the Cohomology of Finite Groups
We will provide an example of a p-group G which has elements of order p in some of its integral cohomology groups but which also has the property that p annihilates H̄(G;Z) for all sufficiently high i. This provides a counterexample to a conjecture of A. Adem which stated that if a finite group K has an element of order p in one of its integral cohomology groups then it has such an element in in...
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ژورنال
عنوان ژورنال: Publications mathématiques de l'IHÉS
سال: 1961
ISSN: 0073-8301,1618-1913
DOI: 10.1007/bf02698718