L. S. Kazarin, V. V. Yanishevskii, “On finite simply reducible groups”, Algebra i Analiz, 19:6 (2007), 86–116; St. Petersburg Math. J., 19:6 (2008), 931

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Algebra i Analiz, 2007, Volume 19, Issue 6, Pages 86–116 (Mi aa147)

This article is cited in 11 scientific papers (total in 11 papers)

Research Papers

On finite simply reducible groups

L. S. Kazarin, V. V. Yanishevskii

P. G. Demidov Yaroslavl State University, Department of Mathematics

Full-text PDF (417 kB) Citations (11)

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Abstract: A finite

G

$G$ group is said to be simply reducible (

S R

$SR$ -group) if it has the following two properties: 1) each element of

G

$G$ is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of

G

$G$ with multiplicities not exceeding 1. It is proved that a finite

S R

$SR$ -group is solvable if it has no composition factors isomorphic to the alternating groups

A_{5}

$A_5$ or

A_{6}

$A_6$ .

Keywords: Group, subgroup, irreducible representation, character, tensor product, real element.

Received: 14.02.2007

English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 6, Pages 931–951
DOI: https://doi.org/10.1090/S1061-0022-08-01028-5

Bibliographic databases:

Document Type: Article

MSC: Primary 53A04; Secondary 52A40, 52A10

Language: Russian

Citation: L. S. Kazarin, V. V. Yanishevskii, “On finite simply reducible groups”, Algebra i Analiz, 19:6 (2007), 86–116; St. Petersburg Math. J., 19:6 (2008), 931–951

Citation in format AMSBIB

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\paper On finite simply reducible groups

\jour Algebra i Analiz

\yr 2007

\vol 19

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\pages 86--116

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\zmath{https://zbmath.org/?q=an:1206.20005}

\transl

\jour St. Petersburg Math. J.

\yr 2008

\vol 19

\issue 6

\pages 931--951

\crossref{https://doi.org/10.1090/S1061-0022-08-01028-5}

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Linking options:

https://www.mathnet.ru/eng/aa147

https://www.mathnet.ru/eng/aa/v19/i6/p86

This publication is cited in the following 11 articles:

Leandro Cagliero, Gonzalo Gutierrez, “G-tables and the Poisson structure of the even cohomology of cotangent bundle of the Heisenberg Lie group”, Journal of Algebra, 2025
Luan Y., “Automorphism Groups of Simply Reducible Groups”, Asian-Eur. J. Math., 14:06 (2021), 2150088
Luan Y., “Examples of Simply Reducible Groups”, J. Korean. Math. Soc., 57:5 (2020), 1187–1237
Kazarin L., “Factorizations of Finite Groups and Related Topics”, Algebr. Colloq., 27:1, SI (2020), 149–180
Ceccherini-Silberstein T., Scarabotti F., Tolli F., “Mackey's Theory of Tau-Conjugate Representations For Finite Groups”, Jap. J. Math., 10:1 (2015), 43–96
Amberg B., Kazarin L., “Large subgroups of a finite group of even order”, Proc. Amer. Math. Soc., 140:1 (2012), 65–68
S. V. Polyakov, “O tenzornykh kvadratakh neprivodimykh predstavlenii konechnykh pochti prostykh grupp. I”, Model. i analiz inform. sistem, 18:1 (2011), 130–141
Polyakov S.V., “O tenzornykh kvadratakh neprivodimykh predstavlenii pochti prostykh grupp s tsokolem, izomorfnym $L_2(Q)$ ”, Vestn. Permskogo un-ta. Ser. Matem. Mekh. Inform., 2011, no. 5, 4–9
S. V. Polyakov, “O tenzornykh kvadratakh neprivodimykh predstavlenii konechnykh pochti prostykh grupp. II”, Model. i analiz inform. sistem, 18:2 (2011), 5–17
L. S. Kazarin, E. I. Chankov, “Finite simply reducible groups are soluble”, Sb. Math., 201:5 (2010), 655–668
L. S. Kazarin, E. I. Chankov, “Priznak abelevosti gruppy nechetnogo poryadka”, Model. i analiz inform. sistem, 16:2 (2009), 103–108

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	85
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