Next Article in Journal
Extraction of Cellulose Nano-Whiskers Using Ionic Liquid-Assisted Ultra-Sonication: Optimization and Mathematical Modelling Using Box–Behnken Design
Previous Article in Journal
Implementation of Block-Based Hierarchical Prediction for Developing an Error-Propagation-Free Reversible Data Hiding Scheme
Open AccessArticle

On Finite Quasi-Core-p p-Groups

by 1,* and 2
1
Basic Course Department, Tianjin Sino-German University of Applied Sciences, Tianjin 300350, China
2
Department of Mathematics, Shanghai University, Shanghai 200444, China
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(9), 1147; https://doi.org/10.3390/sym11091147
Received: 4 August 2019 / Revised: 3 September 2019 / Accepted: 5 September 2019 / Published: 10 September 2019
(This article belongs to the Special Issue Lie Algebras and Groups)
Given a positive integer n, a finite group G is called quasi-core-n if x / x G has order at most n for any element x in G, where x G is the normal core of x in G. In this paper, we investigate the structure of finite quasi-core-p p-groups. We prove that if the nilpotency class of a quasi-core-p p-group is p + m , then the exponent of its commutator subgroup cannot exceed p m + 1 , where p is an odd prime and m is non-negative. If p = 3 , we prove that every quasi-core-3 3-group has nilpotency class at most 5 and its commutator subgroup is of exponent at most 9. We also show that the Frattini subgroup of a quasi-core-2 2-group is abelian. View Full-Text
Keywords: finite p-group; quasi-core-p p-group; commutator subgroup finite p-group; quasi-core-p p-group; commutator subgroup
MDPI and ACS Style

Wang, J.; Guo, X. On Finite Quasi-Core-p p-Groups. Symmetry 2019, 11, 1147.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map

1
Back to TopTop