scholarly journals On the connected components of the spectrums of the character rings of a finite group

2011 ◽  
Vol 328 (1) ◽  
pp. 355-371 ◽  
Author(s):  
Yun Fan ◽  
Xueqin Hu
Keyword(s):  
Finite Group ◽  
Connected Components ◽  
A Finite Group

ON THE POSET OF NON-TRIVIAL PROPER SUBGROUPS OF A FINITE GROUP

2003 ◽  
Vol 02 (02) ◽  
pp. 165-168 ◽  
Author(s):  
MARIA SILVIA LUCIDO
Keyword(s):  
Finite Group ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Connected Components ◽  
Partially Ordered ◽  
Simple Connectivity ◽  
A Finite Group

In this paper we describe the connected components of ℒ(G), the partially ordered set of non-trivial proper subgroups of a finite group G. This result is related to the study of the simple connectivity of the coset poset of a finite group.

scholarly journals CONNECTED COMPONENTS IN THE INVARIABLY GENERATING GRAPH OF A FINITE GROUP

2021 ◽  
pp. 1-11
Author(s):  
DANIELE GARZONI
Keyword(s):  
Finite Group ◽  
Connected Components ◽  
Generating Graph ◽  
A Finite Group

Abstract We prove that the invariably generating graph of a finite group can have an arbitrarily large number of connected components with at least two vertices.

scholarly journals On Thompson’s Conjecture for Alternating GroupsAp+3

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shitian Liu ◽  
Yong Yang
Keyword(s):  
Finite Group ◽  
Prime Graph ◽  
Conjugacy Classes ◽  
Connected Components ◽  
Prime Divisors ◽  
Vertex Set ◽  
Thompson’S Conjecture ◽  
Trivial Center ◽  
A Finite Group

LetGbe a group. Denote byπ(G)the set of prime divisors of|G|. LetGK(G)be the graph with vertex setπ(G)such that two primespandqinπ(G)are joined by an edge ifGhas an element of orderp·q. We sets(G)to denote the number of connected components of the prime graphGK(G). Denote byN(G)the set of nonidentity orders of conjugacy classes of elements inG. Alavi and Daneshkhah proved that the groups,Anwheren=p,p+1,p+2withs(G)≥2, are characterized byN(G). As a development of these topics, we will prove that ifGis a finite group with trivial center andN(G)=N(Ap+3)withp+2composite, thenGis isomorphic toAp+3.

scholarly journals Hurwitz components of groups with socle PSL(3, q)

2021 ◽  
Vol 36 (1) ◽  
pp. 51-62
Author(s):  
H.M. Mohammed Salih
Keyword(s):  
Finite Group ◽  
Monodromy Group ◽  
Riemann Sphere ◽  
Complete List ◽  
Simple Groups ◽  
Connected Components ◽  
Branch Points ◽  
Almost Simple Groups ◽  
Hurwitz Space ◽  
A Finite Group

For a finite group G, the Hurwitz space Hinr,g(G) is the space of genus g covers of the Riemann sphere P1 with r branch points and the monodromy group G. In this paper, we give a complete list of some almost simple groups of Lie rank two. That is, we assume that G is a primitive almost simple groups of Lie rank two. Under this assumption we determine the braid orbits on the suitable Nielsen classes, which is equivalent to finding connected components in Hinr,g(G).

scholarly journals The fundamental group of quotients of products of some topological spaces by a finite group - A generalization of a Theorem of Bauer-Catanese-Grunewald-Pignatelli: Le groupe fondamental de quotients de produits de certains espaces topologiques par ungroupe fini — Généralisation d’un théorème de Bauer–Catanese–Grunewald–Pignatelli

2021 ◽  
Vol Volume 5 ◽  
Author(s):  
Rodolfo Aguilar
Keyword(s):  
Finite Group ◽  
Finite Number ◽  
Fundamental Group ◽  
Universal Cover ◽  
Connected Components ◽  
Topological Spaces ◽  
Group A ◽  
A Finite Group ◽  
Path Connected

We provide a description of the fundamental group of the quotient of a product of topological spaces X i, each admitting a universal cover, by a finite group G, provided that there is only a finite number of path-connected components in X g i for every g ∈ G. This generalizes previous work of Bauer-Catanese-Grunewald-Pignatelli and Dedieu-Perroni. Nous fournissons une description du groupe fondamental du quotient d’un produitd’espaces topologiques Xi , chacun admettant un revêtement universel, par un groupe fini G,pourvu qu’il n’existe qu’un nombre ni de composantes connexes par arcs dans Xgi pour chaque g ∈ G. Cela généralise des résultats antérieurs de Bauer–Catanese–Grunewald–Pignatelli et deDedieu–Perroni.

Finite Groups Whose Common-Divisor Graph is Regular

2018 ◽  
Vol 61 (2) ◽  
pp. 329-341
Author(s):  
Mehdi Ghaffarzadeh ◽  
Mohsen Ghasemi ◽  
Mark L. Lewis
Keyword(s):  
Finite Group ◽  
Regular Graph ◽  
Finite Groups ◽  
Complete Graph ◽  
Solvable Groups ◽  
Connected Components ◽  
Irreducible Characters ◽  
Vertex Set ◽  
The Common ◽  
A Finite Group

AbstractLet G be a finite group, and write cd (G) for the set of degrees of irreducible characters of G. The common-divisor graph Γ(G) associated with G is the graph whose vertex set is cd (G)∖{1} and there is an edge between distinct vertices a and b, if (a, b) > 1. In this paper we prove that if Γ(G) is a k-regular graph for some k ⩾ 0, then for the solvable groups, either Γ(G) is a complete graph of order k + 1 or Γ(G) has two connected components which are complete of the same order and for the non-solvable groups, either k = 0 and cd(G) = cd(PSL2(2f)), where f ⩾ 2 or Γ(G) is a 4-regular graph with six vertices and cd(G) = cd(Alt7) or cd(Sym7).

scholarly journals A DESCRIPTION OF A CLASS OF FINITE SEMIGROUPS THAT ARE NEAR TO BEING MAL'CEV NILPOTENT

2013 ◽  
Vol 12 (05) ◽  
pp. 1250221 ◽  
Author(s):  
E. JESPERS ◽  
M. H. SHAHZAMANIAN
Keyword(s):  
Finite Group ◽  
Algebraic Structure ◽  
Disjoint Union ◽  
Finite Semigroup ◽  
Local Information ◽  
Connected Components ◽  
Global Information ◽  
Nilpotent Ideal ◽  
Finite Semigroups ◽  
A Finite Group

In this paper we continue the investigation on the algebraic structure of a finite semigroup S that is determined by its associated upper non-nilpotent graph [Formula: see text]. The vertices of this graph are the elements of S and two vertices are adjacent if they generate a semigroup that is not nilpotent (in the sense of Mal'cev). We introduce a class of semigroups in which the Mal'cev nilpotent property lifts through ideal chains. We call this the class of pseudo-nilpotent semigroups. The definition is such that the global information that a semigroup is not nilpotent induces local information, i.e. some two-generated subsemigroups are not nilpotent. It turns out that a finite monoid (in particular, a finite group) is pseudo-nilpotent if and only if it is nilpotent. Our main result is a description of pseudo-nilpotent finite semigroups S in terms of their associated graph [Formula: see text]. In particular, S has a largest nilpotent ideal, say K, and S/K is a 0-disjoint union of its connected components (adjoined with a zero) with at least two elements.

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.

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