Finite groups with a unique nonlinear nonfaithful irreducible character

Ali Iranmanesh; Amin Saeidi

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 2, page 91-98
  • ISSN: 0044-8753

Abstract

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In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only p -groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if G is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful irreducible character then G is solvable.

How to cite

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Iranmanesh, Ali, and Saeidi, Amin. "Finite groups with a unique nonlinear nonfaithful irreducible character." Archivum Mathematicum 047.2 (2011): 91-98. <http://eudml.org/doc/116537>.

@article{Iranmanesh2011,
abstract = {In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only $p$-groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if $G$ is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful irreducible character then $G$ is solvable.},
author = {Iranmanesh, Ali, Saeidi, Amin},
journal = {Archivum Mathematicum},
keywords = {minimal normal subgroups; faithful characters; strong condition on normal subgroups; Frobenius groups; nonlinear irreducible characters; finite groups; minimal normal subgroups; faithful characters; Frobenius groups},
language = {eng},
number = {2},
pages = {91-98},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Finite groups with a unique nonlinear nonfaithful irreducible character},
url = {http://eudml.org/doc/116537},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Iranmanesh, Ali
AU - Saeidi, Amin
TI - Finite groups with a unique nonlinear nonfaithful irreducible character
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 2
SP - 91
EP - 98
AB - In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only $p$-groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if $G$ is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful irreducible character then $G$ is solvable.
LA - eng
KW - minimal normal subgroups; faithful characters; strong condition on normal subgroups; Frobenius groups; nonlinear irreducible characters; finite groups; minimal normal subgroups; faithful characters; Frobenius groups
UR - http://eudml.org/doc/116537
ER -

References

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