Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008
qr-code QR
Code

Article

HOME ALL ARTICLES View

J. Korean Math. Soc. 2012; 49(1): 201-221

Printed January 1, 2012

https://doi.org/10.4134/JKMS.2012.49.1.201

Copyright © The Korean Mathematical Society.

Nomalizers of nonnormal subgroups of finite $p$-groups

Qinhai Zhang and Juan Gao

Shanxi Normal University, Shanxi Normal University

Abstract

Go to

Assume $G$ is a finite $p$-group and $i$ is a fixed positive integer. In this paper, finite $p$-groups $G$ with $|N_G(H): H|=p^i$ for all nonnormal subgroups $H$ are classified up to isomorphism. As a corollary, this answers Problem 116(i) proposed by Y. Berkovich in his book ``Groups of Prime Power Order Vol. I" in 2008.

Keywords: finite $p$-groups, nonnormal subgroups, self-normalizer, central extensions

MSC numbers: Primary 20D15, 20E99

Article Tools

Stats or Metrics

Share this article on :

Related articles in JKMS

more +