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Open AccessArticle

On Finite Quasi-Core-p p-Groups

by 1,* and 2
Basic Course Department, Tianjin Sino-German University of Applied Sciences, Tianjin 300350, China
Department of Mathematics, Shanghai University, Shanghai 200444, China
Author to whom correspondence should be addressed.
Symmetry 2019, 11(9), 1147;
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.

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