SOLVABLE GROUPS WHOSE NONNORMAL SUBGROUPS HAVE FEW ORDERS

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-27 DOI:10.1017/s0004972723001168

LIJUAN HE, HENG LV, GUIYUN CHEN

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引用次数: 0

Abstract

Suppose that G is a finite solvable group. Let

$t=n_c(G)$

denote the number of orders of nonnormal subgroups of G. We bound the derived length

$dl(G)$

in terms of

$n_c(G)$

. If G is a finite p-group, we show that

$|G'|\leq p^{2t+1}$

and

$dl(G)\leq \lceil \log _2(2t+3)\rceil $

. If G is a finite solvable nonnilpotent group, we prove that the sum of the powers of the prime divisors of

$|G'|$

is less than t and that

$dl(G)\leq \lfloor 2(t+1)/3\rfloor +1$

查看原文本刊更多论文

非正常子群阶数少的可解群

假设 G 是一个有限可解群。让 $t=n_c(G)$ 表示 G 的非正则子群的阶数。我们用 $n_c(G)$ 约束派生长度 $dl(G)$ 。如果 G 是有限 p 群，我们证明 $|G'|\leq p^{2t+1}$ 和 $dl(G)\leq \lceil \log _2(2t+3)\rceil $ 。如果 G 是一个有限可解的非幂群，我们证明 $|G'|$ 的素除数的幂和小于 t 并且 $dl(G)\leq \lfloor 2(t+1)/3\rfloor +1$ .

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society