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## Irr(G|N) and Solvability

SUN GuanghongCollege of Science, Hehai University, Nanjing Jiangsu 210098, China
It is investigated that the restricted set of irreducible characters Irr(G|N) has influences on the solvability of a normal subgroup N. And some simple structures of N is dealed with. Some principal results are obtained as followings:Theorem 1Let NG. If each character of Irr(G|N) is Smonomial, then N is Sgroup.Theorem 2Let NG such that for each χ∈ Irr (G|N), there exists H≤G and λ∈ Irr (H) such that λ=λG and H/Kerλ is solvable. Then N is solvable.Theorem 6Let S be a set of simple groups containing groups of all prime orders, NG and a=max(cd(G|N)). For each χ∈Irr(G|N) and χ(1)a, if λ is Smonomial, then N is solvable.Theorem 8Let G is monolith and NG. For a prime number p, if p|χ(1) for each λ of Irrm(G|N), then N exists a normal pcomplement and N is solvable.
【CateGory Index】： O152.6
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 【Citations】
 Chinese Journal Full-text Database 1 Hits
 1 SUN Guanghong Dept. of Mathematics, Southwest China Normal University, Chongqing 400715, China;Properties of Irr(G｜N)[J];西南师范大学学报(自然科学版);2001-06
 【Co-citations】
 Chinese Journal Full-text Database 1 Hits
 1 SUN GuanghongCollege of Science, Hehai University, Nanjing Jiangsu 210098, China;Irr(G|N) and Solvability[J];西南师范大学学报(自然科学版);2003-01
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