scholarly journals On the connected components of the spectrum of the extended character ring of a finite group

2007 ◽  
Vol 312 (2) ◽  
pp. 689-698 ◽  
Author(s):  
Gang Chen ◽  
Yun Fan
Keyword(s):  
Finite Group ◽  
Connected Components ◽  
A Finite Group ◽  
Character Ring

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.

Ring of classes and character ring of a finite group

1979 ◽  
Vol 26 (1) ◽  
pp. 493-499
Author(s):  
A. I. Saksonov
Keyword(s):  
Finite Group ◽  
A Finite Group ◽  
Character Ring

scholarly journals The character ring of a finite group

1965 ◽  
Vol 9 (3) ◽  
pp. 462-467 ◽  
Author(s):  
Donald R. Weidman
Keyword(s):  
Finite Group ◽  
A Finite Group ◽  
Character Ring

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.

On the Character Rings of Finite Groups

1963 ◽  
Vol 15 ◽  
pp. 605-612 ◽  
Author(s):  
B. Banaschewski
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Characteristic Zero ◽  
Irreducible Representations ◽  
Roots Of Unity ◽  
Closed Field ◽  
One Dimensional ◽  
Elementary Group ◽  
A Finite Group ◽  
Character Ring

The characters of the representations of a finite group G over a field K of characteristic zero generate a ring oK(G) of functions on G, the K-character ring of G, which is readily seen to be Zϕ1 + . . . + Zϕn, where Z is the ring of rational integers and ϕ1, . . . , ϕn are the characters of the different irreducible representations of G over K. The theorem that every irreducible representation of G over an algebraically closed field Ω of characteristic zero is equivalent to a representation of G over the subfield of Ω which is generated by the g0th roots of unity (g0 the exponent of G) was proved by Brauer (4) via the theorems that(1) OΩ(G) is additively generated by the induced characters of representations of elementary subgroups of G, and(2) the irreducible representations over 12 of any elementary group are induced by one-dimensional subgroup representations (3).

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).

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