Volume 6 Number 4 (Oct. 2016)
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IJAPM 2016 Vol.6(4): 194-199 ISSN: 2010-362X
doi: 10.17706/ijapm.2016.6.4.194-199

On π-nilpotency of Finite Groups

Rongge Yu, Ruixia Jiang
Abstract—A group G is called л-nilpotent, л a set of primes, if G has a normal л’-subgroup N with G/N a nilpotent л-group. Let H be a nilpotent л-Hall subgroup of G, 1<Z1(H)<Z2(H) <┄<Zn(H)=H be the upper central series of H. If every Zi(H) is weakly closed in H (about G). Then we say that the upper central series of H is weakly closed in H (about G). Let H be a subgroup of a finite group G. We call H weakly s-normal in G if there exists a Sylow p-subgroup Sp which is permutable with H for every prime p∣|G|. In this paper, with the conception above, several determine theorems for G to be a л─nilpotent group are given and some properties about л─nilpotent groups are considered. Several results about nilpotent groups are generalized.

Index Terms—л─nilpotent groups, minimal normal subgroups, л-normal groups, weakly s-normal subgroups.

The authors are with School of Mathematics and Statistics, Cangzhou Normal University, Cangzhou, China (email: yurongge999@163.com.).

Cite: Rongge Yu, Ruixia Jiang, "On π-nilpotency of Finite Groups," International Journal of Applied Physics and Mathematics vol. 6, no. 4, pp. 194-199, 2016.

General Information

ISSN: 2010-362X
Frequency: Bimonthly (2011-2014); Quarterly (Since 2015)
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca
Abstracting/ Indexing: Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Electronic Journals Library, Engineering & Technology Digital Library, Nanowerk Database, Google Scholar and ProQuest
E-mail: ijapm@iap.org
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