Normal subgroups contained in Frattini subgroups are Frattini subgroups-Reference-Cited by-同舟云学术

Normal subgroups contained in Frattini subgroups are Frattini subgroups

Published:1980 Issue:3 Volume:78 Page:315-318
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Allenby R. B. J. T.

Abstract

We prove that if N is a normal subgroup of the finite group G and if N ⊆ Φ ( G ) N \subseteq \Phi (G) , then there exists a finite group U such that N = Φ ( U ) N = \Phi (U) exactly. In particular, we see that the generalizations apparent in the conclusions of several recently stated theorems are illusory.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1980-078-03/S0002-9939-1980-0553365-1/S0002-9939-1980-0553365-1.pdf

Reference10 articles.

1. On the Frattini subgroups of generalized free products;Allenby, R. B. J. T.;J. Algebra,1978

2. Über die Φ-Untergruppe endlicher Gruppen;Gaschütz, Wolfgang;Math. Z.,1953

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

4. Normal subgroups contained in the Frattini subgroup;Hill, W. Mack;Proc. Amer. Math. Soc.,1972

5. Die Untergruppen der freien Produkte von beliebigen Gruppen;Kurosch, Alexander;Math. Ann.,1934

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