Finite groups with an irreducible representation of large degree

1969 ◽  
Vol 108 (2) ◽  
pp. 145-153 ◽  
Author(s):  
Frank R. DeMeyer ◽  
Gerald J. Janusz
Keyword(s):  
Irreducible Representation ◽  
Finite Groups ◽  
Large Degree

scholarly journals A Remark on the Orthogonality Relations in the Representation Theory of Finite Groups

1959 ◽  
Vol 11 ◽  
pp. 59-60 ◽  
Author(s):  
Hirosi Nagao
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Representation Theory ◽  
Finite Groups ◽  
Characteristic Zero ◽  
Orthogonality Relations ◽  
Schur’S Lemma ◽  
Image Position ◽  
A Finite Group ◽  
Schur's Lemma

Let G be a finite group of order g, andbe an absolutely irreducible representation of degree fμ over a field of characteristic zero. As is well known, by using Schur's lemma (1), we can prove the following orthogonality relations for the coefficients :1It is easy to conclude from (1) the following orthogonality relations for characters:whereand is 1 or 0 according as t and s are conjugate in G or not, and n(t) is the order of the normalize of t.

scholarly journals Finite groups with an irreducible character of large degree

2015 ◽  
Vol 149 (3-4) ◽  
pp. 523-546 ◽  
Author(s):  
Nguyen Ngoc Hung ◽  
Mark L. Lewis ◽  
Amanda A. Schaeffer Fry
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Large Degree

UNIPOTENT ELEMENTS IN REPRESENTATIONS OF FINITE GROUPS OF LIE TYPE

2012 ◽  
Vol 11 (02) ◽  
pp. 1250038 ◽  
Author(s):  
L. DI MARTINO ◽  
A. E. ZALESSKI
Keyword(s):  
Normal Subgroup ◽  
Irreducible Representation ◽  
Simple Group ◽  
Finite Groups ◽  
Closed Field ◽  
Group Of Lie Type ◽  
Algebraically Closed Field ◽  
Central Quotient ◽  
Representations Of Finite Groups ◽  
Groups Of Lie Type

Let G be a finite quasi-simple group of Lie type of defining characteristic r > 2. Let H = 〈h, G〉 be a group with normal subgroup G, where h is a non-central r-element of H. Let ϕ be an irreducible representation of H non-trivial on G over an algebraically closed field of characteristic ℓ ≠ r. We show that ϕ(h) has at least two distinct eigenvalues of multiplicity greater than 1, unless G is a central quotient of one of the following groups: SL(2, r), SL(2, 9) or Sp(4, 3), and H = G⋅Z(H).

scholarly journals Infinite groups admitting a faithful irreducible representation

2018 ◽  
Vol 17 (01) ◽  
pp. 1850005
Author(s):  
Fernando Szechtman ◽  
Anatolii Tushev
Keyword(s):  
Irreducible Representation ◽  
Finite Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Necessary And Sufficient

Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated. We consider locally finite groups and groups whose socle is essential.

Finite Groups with Only One NonLinear Irreducible Representation

2012 ◽  
Vol 40 (11) ◽  
pp. 4324-4329 ◽  
Author(s):  
Silvio Dolfi ◽  
Gabriel Navarro
Keyword(s):  
Irreducible Representation ◽  
Finite Groups

scholarly journals Geometry of Group Representations

1966 ◽  
Vol 27 (2) ◽  
pp. 509-513 ◽  
Author(s):  
G. De B. Robinson
Keyword(s):  
Irreducible Representation ◽  
Finite Groups ◽  
Group Representations ◽  
Tensor Power ◽  
The Many

The many unanswerable questions (1) which arise in the study of finite groups have lead to a review of fundamental ideas, e.g. the Theorem of Burnside (3, p. 299; 2, 6) that if λ be any faithful irreducible representation of G over a field K, then every irreducible representation of G over K is contained in some tensor power of λ.

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