FINITE p-GROUPS IN WHICH THE NORMAL CLOSURES OF THE NON-NORMAL CYCLIC SUBGROUPS HAVE SMALL INDEX-Reference-Cited by-同舟云学术

FINITE p-GROUPS IN WHICH THE NORMAL CLOSURES OF THE NON-NORMAL CYCLIC SUBGROUPS HAVE SMALL INDEX

Published:2013-10-10 Issue:02 Volume:13 Page:1350087
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

ZHAO LIBO¹,GUO XIUYUN¹

Affiliation:

1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

Abstract

A p-group is called a C(pw)-group if the normal closure of every non-normal cyclic subgroup has index at most pw. In this paper, we prove that the order of a non-Dedekind C(pw)-group cannot exceed p4w+4 when p > 2 and G′ ≤ HG for every non-normal cyclic subgroup H. We also completely classify non-Dedekind C(p2)-groups for p > 2.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498813500874

Reference8 articles.

1. The Magma Algebra System I: The User Language

2. On Generalized Dedekind Groups and Tarski Super Monsters

3. Some finite p-groups with bounded index of every cyclic subgroup in its normal closure

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Finite p -groups in which the intersection of nonnormal subgroup and center has bounded order;Communications in Algebra;2023-03-23

2. On Finite NDC-Groups;Bulletin of the Malaysian Mathematical Sciences Society;2019-11-11

3. FINITE -GROUPS ALL OF WHOSE NONNORMAL SUBGROUPS HAVE BOUNDED NORMAL CORES;Bulletin of the Australian Mathematical Society;2019-07-18

4. On finite p-groups with few normal subgroups;Journal of Algebra and Its Applications;2016-08-17

5. Finitep-Groups All of Whose Minimal Nonnormal Subgroups Posses Large Normal Closures;Communications in Algebra;2015-11-13