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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 223, Pages 108–119
(Mi znsl4359)
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This article is cited in 2 scientific papers (total in 2 papers)
Representation theory
Transitive groups with irreducible representations of bounded degree
S. A. Evdokimova, I. N. Ponomarenkob a St. Petersburg Institute for Informatics and Automation, Russian Academy of Sciences
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
A well-known theorem of Jordan states that there ezists a function $J(d)$ of a positive integer $d$ for which the following holds: if $G$ is a finite group having a faithful linear representation over $\mathbb C$ of degree $d$, then $G$ has a normal Abelian subgroup $A$ with $[G:A]\le J(d)$. We show that if $G$ is a transitive permutation group and $d$ is the maximal degree of irreducible representations of $G$ entering its permutation representation, then there exists a normal solvable subgroup $A$ of $G$ such that $[G:A]\le J(d)^{\log_2d}$. Bibliography: 7 titles.
Received: 15.05.1995
Citation:
S. A. Evdokimov, I. N. Ponomarenko, “Transitive groups with irreducible representations of bounded degree”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Zap. Nauchn. Sem. POMI, 223, POMI, St. Petersburg, 1995, 108–119; J. Math. Sci. (New York), 87:6 (1997), 4046–4053
Linking options:
https://www.mathnet.ru/eng/znsl4359 https://www.mathnet.ru/eng/znsl/v223/p108
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Abstract page: | 124 | Full-text PDF : | 47 |
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