Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character

Amin Saeidi

Open Mathematics (2014)

  • Volume: 12, Issue: 1, page 79-83
  • ISSN: 2391-5455

Abstract

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In this note, we study finite groups possessing exactly one nonlinear non-faithful irreducible character. Our main result is to classify solvable groups that satisfy this property. Also, we give examples to show that these groups need not to be solvable in general.

How to cite

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Amin Saeidi. "Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character." Open Mathematics 12.1 (2014): 79-83. <http://eudml.org/doc/269696>.

@article{AminSaeidi2014,
abstract = {In this note, we study finite groups possessing exactly one nonlinear non-faithful irreducible character. Our main result is to classify solvable groups that satisfy this property. Also, we give examples to show that these groups need not to be solvable in general.},
author = {Amin Saeidi},
journal = {Open Mathematics},
keywords = {Minimal normal subgroups; Non-faithful characters; Frobenius groups; nonlinear irreducible characters; finite groups; finite solvable groups; minimal normal subgroups; non-faithful characters},
language = {eng},
number = {1},
pages = {79-83},
title = {Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character},
url = {http://eudml.org/doc/269696},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Amin Saeidi
TI - Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character
JO - Open Mathematics
PY - 2014
VL - 12
IS - 1
SP - 79
EP - 83
AB - In this note, we study finite groups possessing exactly one nonlinear non-faithful irreducible character. Our main result is to classify solvable groups that satisfy this property. Also, we give examples to show that these groups need not to be solvable in general.
LA - eng
KW - Minimal normal subgroups; Non-faithful characters; Frobenius groups; nonlinear irreducible characters; finite groups; finite solvable groups; minimal normal subgroups; non-faithful characters
UR - http://eudml.org/doc/269696
ER -

References

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  1. [1] Aschbacher M., Finite Group Theory, Cambridge Stud. Adv. Math., 10, Cambridge University Press, Cambridge, 1986 
  2. [2] Iranmanesh A., Saeidi A., Finite groups with a unique nonlinear nonfaithful irreducible character, Arch. Math. (Brno), 2011, 47(2), 91–98 Zbl1249.20009
  3. [3] Seitz G.M., Finite groups having only one irreducible representation of degree greater than one, Proc. Amer. Math. Soc., 1968, 19, 459–461 http://dx.doi.org/10.1090/S0002-9939-1968-0222160-X Zbl0244.20010

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