Normal subgroups contained in the Frattini subgroup. II-Reference-Cited by-同舟云学术

Normal subgroups contained in the Frattini subgroup. II

Published:1975 Issue:2 Volume:53 Page:277-279
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Hill W. Mack

Abstract

If p p is an odd prime and H H is a p p -group with a characteristic subgroup K K such that | K | > | K ∩ Z ( H ) | = p |K| > |K \cap Z(H)| = p , then H H cannot be a normal subgroup contained in the Frattini subgroup of any finite group G G .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1975-053-02/S0002-9939-1975-0390051-3/S0002-9939-1975-0390051-3.pdf

Reference8 articles.

1. Automorphisms of extra special groups and nonvanishing degree 2 cohomology;Griess, Robert L., Jr.;Pacific J. Math.,1973

2. Frattini subgroups of 𝑝-closed and 𝑝-supersolvable groups;Hill, W. Mack;Israel J. Math.,1974

3. \bysame, Extra-special normal 𝑝-subgroups, Notices Amer. Math. Soc. 21 (1974), A-526. Abstract #74T-A214.

4. The nilpotence class of the Frattini subgroup;Hill, W. Mack;Israel J. Math.,1973

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1. Finite groups;Journal of Soviet Mathematics;1989-02

2. On normalp-subgroups with large centers which cannot be contained in the Frattini subgroup;Israel Journal of Mathematics;1978-06

3. Zerfall von Automorphismengruppen endlicher Gruppen;Archiv der Mathematik;1977-12

4. Frattini subgroups and supernilpotent groups;Israel Journal of Mathematics;1977-03