On the Taketa Theorem
On the Taketa Theorem
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DOI：
10.1006/jabr.1996.0183
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发表时间：
1996-06
影响因子：
0.9
通讯作者：
Y. Berkovich
中科院分区：
文献类型：
--
作者：
Y. Berkovich
Abstract In this note we prove that a finite group is almost solvable if every irreducible character is induced from a character of degree at most 4 (more precisely, such a groupGis solvable, orG/S(G)≅A5, where S(G) is the solvable radical ofG). In particular, if every irreducible character ofGis induced from a character of degree at most 3 thenGis solvable. This result justifies Conjecture 3 from a previous paper by the author (Proc. Amer. Math. Soc.1231 (1995), 3263–3268). Our proofs use the fact that A5(≅PSL(2.5)) and PSL(2, 7) are the only complex linear nonabelian simple groups of degree at most 4.
