The irreducible characters of 𝑆ⁿ

2002 ◽  
pp. 33-35
Author(s):  
David Goldschmidt
Keyword(s):  
Irreducible Characters

ON HIGHER FROBENIUS–SCHUR INDICATORS

2021 ◽  
pp. 1-11
Author(s):  
YANJUN LIU ◽  
WOLFGANG WILLEMS
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Irreducible Characters ◽  
A Finite Group

Abstract Similarly to the Frobenius–Schur indicator of irreducible characters, we consider higher Frobenius–Schur indicators $\nu _{p^n}(\chi ) = |G|^{-1} \sum _{g \in G} \chi (g^{p^n})$ for primes p and $n \in \mathbb {N}$ , where G is a finite group and $\chi $ is a generalised character of G. These invariants give answers to interesting questions in representation theory. In particular, we give several characterisations of groups via higher Frobenius–Schur indicators.

The quotient of two Glauberman–Isaacs correspondences

2016 ◽  
Vol 15 (07) ◽  
pp. 1650138
Author(s):  
Alexandre Turull ◽  
Thomas R. Wolf
Keyword(s):  
Finite Group ◽  
Irreducible Characters ◽  
A Finite Group

Let a finite group [Formula: see text] act coprimely on a finite group [Formula: see text]. The Glauberman–Isaacs correspondence [Formula: see text] is a bijection from the set of [Formula: see text]-invariant irreducible characters of [Formula: see text] onto the set [Formula: see text] of irreducible characters of the centralizer of [Formula: see text] in [Formula: see text]. Let [Formula: see text] be a subgroup of [Formula: see text]. Composing from left to right, it follows that [Formula: see text] is an injection from [Formula: see text] into [Formula: see text]. We show that, in some cases, the map can be defined via the actions of some subgroups of [Formula: see text] containing [Formula: see text] on the centralizers in [Formula: see text] of some other such subgroups. We also show in many instances, such as [Formula: see text] odd or [Formula: see text] supersolvable and [Formula: see text] solvable, that this map is independent of the overgroup [Formula: see text].

Irreducible characters of the group S n that are semiproportional on A n

Algebra and Logic ◽  
2008 ◽  
Vol 47 (2) ◽  
pp. 77-90 ◽  
Author(s):  
V. A. Belonogov
Keyword(s):  
Irreducible Characters

scholarly journals Defects of Irreducible Characters ofp-Soluble Groups

Journal of Algebra ◽  
1998 ◽  
Vol 202 (1) ◽  
pp. 178-184 ◽  
Author(s):  
Laurence Barker
Keyword(s):  
Soluble Groups ◽  
Irreducible Characters

On Finite Groups with an Abelian Sylow Group

1962 ◽  
Vol 14 ◽  
pp. 436-450 ◽  
Author(s):  
Richard Brauer ◽  
Henry S. Leonard
Keyword(s):  
Finite Groups ◽  
Irreducible Characters ◽  
Collineation Groups ◽  
Sylow Group

We shall consider finite groups of order of g which satisfy the following condition:(*) There exists a prime p dividing g such that if P ≠ 1 is an element of p-Sylow group ofthen the centralizer(P) of P incoincides with the centralizer() of in.This assumption is satisfied for a number of important classes of groups. It also plays a role in discussing finite collineation groups in a given number of dimensions.Of course (*) implies that is abelian. It is possible to obtain rather detailed information about the irreducible characters of groups in this class (§ 4).

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