On finite simply reducible groups
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L. S. Kazarin and V. V. Yanishevskiĭ
Translated by: B. M. Bekker - St. Petersburg Math. J. 19 (2008), 931-951
- DOI: https://doi.org/10.1090/S1061-0022-08-01028-5
- Published electronically: August 21, 2008
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Abstract:
A finite group $G$ is said to be simply reducible ($SR$-group) if it has the following two properties: 1) each element of $G$ is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of $G$ with multiplicities not exceeding 1. It is proved that a finite $SR$-group is solvable if it has no composition factors isomorphic to the alternating groups $A_5$ or $A_6$.References
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Bibliographic Information
- L. S. Kazarin
- Affiliation: Mathematics Department, Yaroslavl Demidov State University, Sovetskaya 14, Yaroslavl 150000, Russia
- Email: kazarin@uniyar.ac.ru
- V. V. Yanishevskiĭ
- Affiliation: Mathematics Department, Yaroslavl Demidov State University, Sovetskaya 14, Yaroslavl 150000, Russia
- Email: yvitaliy@rambler.ru
- Received by editor(s): February 14, 2007
- Published electronically: August 21, 2008
- Additional Notes: The first author was supported by RFBR (grant no. 05-01-01018)
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 931-951
- MSC (2000): Primary 53A04; Secondary 52A40, 52A10
- DOI: https://doi.org/10.1090/S1061-0022-08-01028-5
- MathSciNet review: 2411640
Dedicated: Dedicated to the centenary of D. K. Faddeev’s birth