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On the norm of the derived‎ subgroups of all subgroups of a finite group

Article 17, Volume 40, Issue 1, February 2014, Page 281-291  XML PDF (118 K)
Document Type: Research Paper
Authors
Zhencai Shen1; Shirong Li2; Wujie Shi 3
1LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China.
2Guangxi University
3Chongqing University of Arts and Sciences
Abstract
In this paper‎, ‎we give a complete proof of Theorem 4.1(ii) and a new‎ ‎elementary proof of Theorem 4.1(i) in [Li and Shen‎, ‎On the‎ ‎intersection of the normalizers of the derived subgroups of all‎
‎subgroups of a finite group‎, ‎ J‎. ‎Algebra, ‎323  (2010) 1349--1357]‎.
‎In addition‎, ‎we also give a generalization of Baer's Theorem‎.
Keywords
Derived subgroup; Solvable group; nilpotency class; Fitting length
Main Subjects
20-XX Group theory and generalizations
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