Normal Subgroups Contained in the Frattini Subgroup

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Oct 1972Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 35, page 413 (issn: 0002-9939,

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Authors: Hill, W. Mack; Wright, Charles R. B.;

doi: 10.2307/2037619 , 10.1090/s0002-9939-1972-0301094-7

Normal Subgroups Contained in the Frattini Subgroup

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Abstract

Let H be a normal subgroup of the finite group G. If H has a subgroup K which is normal in G, satisfies | K | > | K ∩ Z 1 ( H ) | = p |K| > |K \cap {Z_1}(H)| = p and is not of nilpotence class 2, then H is not contained in the Frattini subgroup of G.

Keywords

Special subgroups (Frattini, Fitting, etc.), Finite nilpotent groups, \(p\)-groups

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