On the Norm of the Abelian p-Group-Residuals

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 13 Apr 2021 English Publisher:MDPI AGJournal:Mathematics, volume 9, page 842 (eissn: 2227-7390,

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Authors: Baojun Li; Yu Han; Lü Gong; Tong Jiang;

doi: 10.3390/math9080842

On the Norm of the Abelian p-Group-Residuals

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Abstract

Let G be a group. Dp(G)=⋂H≤GNG(H′(p)) is defined and, the properties of Dp(G) are investigated. It is proved that Dp(G)=P[A], where P=D(P) is the Sylow p-subgroup and A=N(A) is a Hall p′-subgroup of Dp(G), respectively. Furthermore, it is proved in a group G that (1) Dp(G)=1 if and only if CG(G′(p))=1; (2) Op′(Dp(G))≤Z∞(Op(G)) and (3) if Z(G′(p))=1, then CG(G′(p))=Dp(G).

Related Organizations

Nantong University
China (People's Republic of)

Keywords

normalizer, finite group, QA1-939, soluble group, abelian p-group residual, Mathematics

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