Transitive groups with irreducible representations of bounded degree
- Cite this article as:
- Evdokimov, S.A. & Ponomarenko, I.N. J Math Sci (1997) 87: 4046. doi:10.1007/BF02355798
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A well-known theorem of Jordan states that there exists 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 ℂ of degree d, then G has a normal Abelian subgroup A with [G:A]≤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]≤J(d)log2d. Bibliography: 7 titles.