arXiv 0812.22202008-12-11math.GR

所有irreducible characters都是超单项式的群

Groups where all the irreducible characters are super-monomial

Mark L. Lewis

摘要：

Isaacs定义了一个特征标是超单名的，如果它的每个本原特征标都是线性的。Isaacs证明了：如果$G$是奇阶$M$ -群，则每个不可约特征标都是超单项式.证明了如果$G$是奇数阶$M$ -群，其中每个不可约特征标是某个素数$p$的$\{p \}$ -提升，则该猜想成立.我们说一个群的不可约特征标是超单项式，它是一个超$M$ -群。我们使用我们的结果找到一个例子的超级$M$ -组，有一个子群，这不是一个超级$M$ -组。

英文摘要：

Isaacs has defined a character to be super monomial if every primitive character inducing it is linear. Isaacs has conjectured that if $G$ is an $M$-group with odd order, then every irreducible character is super monomial. We prove that the conjecture is true if $G$ is an $M$-group of odd order where every irreducible character is a $\{p \}$-lift for some prime $p$. We say that a group where irreducible character is super monomial is a super $M$-group. We use our results to find an example of a super $M$-group that has a subgroup that is not a super $M$-group.

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