Results 11 to 20 of about 1,287 (264)

GVZ-groups, Flat groups, and CM-Groups

Comptes Rendus. Mathématique, 2021
We show that a group is a GVZ-group if and only if it is a flat group. We show that the nilpotence class of a GVZ-group is bounded by the number of distinct degrees of irreducible characters.
Burkett, Shawn T., Lewis, Mark L.
doaj   +1 more source

Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters [PDF]

AUT Journal of Mathematics and Computing, 2023
For a character $ \chi $ of a finite group $ G $, the number $ \chi^c(1)=\frac{[G:{\rm ker}\chi]}{\chi(1)} $ is called the co-degree of $ \chi $. Let ${\rm Sol}(G)$ denote the solvable radical of $G$.
Neda Ahanjideh
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Products of Irreducible Characters Having Complex-Valued Constituents [PDF]

Advances in Group Theory and Applications, 2017
First, we prove that when a finite solvable group $G$ has a faithful irreducible character $\chi$ such that $\chi\overline{\chi}$ has two irreducible constituents, both must be real-valued.
Lisa R. Hendrixson, Mark L. Lewis
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Finite Groups Having Monolithic Characters of Prime Degree

Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2021
Let G be a finite group. An irreducible character χ is called monolithic when the factor group G/ker⁡(χ) has unique minimal normal subgroup. In this paper, we prove that for the smallest prime q dividing the order of G if G has a faithful imprimitive ...
Temha Erkoç, Burcu Çınarcı
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The χ–Subgroups of Special linear group SL(n,q) [PDF]

مجلة جامعة الانبار للعلوم الصرفة, 2012
In this paper we find χ-subgroup for the irreducible characters χ of the Special linear group SL(n,q) when n=2 ...
Afrah M. Ibraheem
doaj   +1 more source

Some Remarks on Anchor of Irreducible Characters [PDF]

Advances in Group Theory and Applications
In this paper, we show that the direct product of the anchors of two irreducible characters is the anchor of the tensor product of their irreducible characters. We prove that the anchor of any irreducible character of a p-group G is G itself.
Manal H. Algreagri, Ahmad M. Alghamdi
doaj   +1 more source

On Sums of Degrees of Irreducible Characters

Journal of Algebra, 1998
Let \(G\) be a finite group, \(\text{Irr}(G)=\{\chi^1,\dots,\chi^k\}\), and put \(\tau=\sum_{i=1}^k\chi^i\) and \(T(G)=\tau(1)\). If \(H\) is a nontrivial subgroup of \(G\), let \(a=\langle\tau_H,1_H\rangle\), \(\delta(G,H)=T(G)-T(H)\) and \(\delta_0(G,H)=\delta(G,H)-(a-1)\).
Berkovich, Yakov, Mann, Avinoam
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On degrees of irreducible Brauer characters [PDF]

Transactions of the American Mathematical Society, 2004
Based on a large amount of examples, which we have checked so far, we conjecture that | G
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On the orders of zeros of irreducible characters

Journal of Algebra, 2009
Let \(G\) be a finite group. \(g\in G\) is called a vanishing element if \(\chi(g)=0\) for some irreducible character of \(G\). The main result of the paper under review is that if \(p\) is a prime and \(G\) does not have any vanishing element of \(p\)-power order, then \(G\) has a normal Sylow \(p\)-subgroup.
DOLFI, SILVIO, E. Pacifici, L. Sanus, P. Spiga   +3 more
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On the Irreducible Characters of Hecke Algebras

Advances in Mathematics, 1993
Let \(W\) be a finite Weyl group, and \(K\) an arbitrary field. Let \(H_ K\) be the Hecke algebra associated with \(W\) over \(K\) with parameters \(q_ s\), \(s \in S\), where \(S \subset W\) is a corresponding set of simple reflections. The authors show that the values of the irreducible characters are constant on basis elements \(T_ w\), where \(w ...
Geck, M., Pfeiffer, G.
openaire   +1 more source