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Mat. Zametki, 2015, Volume 98, Issue 2, Pages 237–246 (Mi mz10605)  

This article is cited in 4 scientific papers (total in 4 papers)

Finite Groups with Large Irreducible Character

L. S. Kazarin, S. S. Poiseeva

P. G. Demidov Yaroslavl State University

Abstract: In the general case, the order of a finite nonidentity group $G$ is substantially larger than the squared degree of every irreducible character $\Theta$ of $G$, i.e., $\Theta(1)^2<|G|$. In the present paper, we study finite groups with an irreducible character $\Theta$ such that
$$ |G|\le 2\Theta(1)^2. $$


Keywords: finite group, irreducible character, Frobenius group, Sylow subgroup, constituent, Galois group, Clifford theory, Fitting subgroup.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00469
The work of the first author was financially supported by the Russian Foundation for Basic Research (grant no. 13-01-00469).


DOI: https://doi.org/10.4213/mzm10605

Full text: PDF file (468 kB)
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English version:
Mathematical Notes, 2015, 98:2, 265–272

Bibliographic databases:

UDC: 512.547.214
Received: 12.09.2014
Revised: 08.02.2015

Citation: L. S. Kazarin, S. S. Poiseeva, “Finite Groups with Large Irreducible Character”, Mat. Zametki, 98:2 (2015), 237–246; Math. Notes, 98:2 (2015), 265–272

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. S. Kazarin, S. S. Poiseeva, “O konechnykh gruppakh s bolshoi stepenyu neprivodimogo kharaktera”, Model. i analiz inform. sistem, 22:4 (2015), 483–499  mathnet  crossref  mathscinet  elib
    2. L. S. Kazarin, S. S. Poiseeva, “On finite groups with large degrees of irreducible character”, Autom. Control Comp. Sci., 50:7 (2016), 497–509  crossref  isi  scopus
    3. S. S. Poiseeva, “O stroenii konechnykh grupp s bolshim neprivodimym kharakterom stepeni $p^2q$”, Matematicheskie zametki SVFU, 23:3 (2016), 81–90  mathnet  elib
    4. S. S. Poiseeva, “A bound on the order of finite groups with large irreducible character”, Proceedings of the 8th International Conference on Mathematical Modeling (ICMM-2017), AIP Conference Proceedings, v. 1907, eds. I. E. Egorov, S. V. Popov, P. N. Vabishchevich, M. Yu. Antonov, N. P. Lazarev, M. S. Troeva, A. O. I, Amer Inst Physics, 2017, UNSP 030053-1  crossref  isi  scopus
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