On a Generalization of Hamiltonian Groups and a Dualization of PN-Groups |
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Authors: | Zhencai Shen Jinshan Zhang Wujie Shi |
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Institution: | 1. LMAM and School of Mathematical Sciences , Peking University , Beijing , China zhencai688@sina.com;3. School of Science , Sichuan University of Science and Engineering , Zigong , China;4. Department of Mathematics and Statistics , Chongqing University of Arts and Sciences , Chongqing , China |
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Abstract: | Baer and Wielandt in 1934 and 1958, respectively, considered that the intersection of the normalizers of all subgroups of G and the intersection of the normalizers of all subnormal subgroups of G. In this article, for a finite group G, we define the subgroup S(G) to be intersection of the normalizers of all non-cyclic subgroups of G. Groups whose noncyclic subgroups are normal are studied in this article, as well as groups in which all noncyclic subgroups are normalized by all minimal subgroups. In particular, we extend the results of Passman, Bozikov, and Janko to non-nilpotent finite groups. |
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Keywords: | Derived subgroup Fitting length Nilpotency class Solvable group |
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