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

Normal subgroups contained in the Frattini subgroup

Published:1972 Issue:2 Volume:35 Page:413-415
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Hill W. Mack,Wright Charles R. B.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-035-02/S0002-9939-1972-0301094-7/S0002-9939-1972-0301094-7.pdf

Reference3 articles.

1. Die Grundlehren der mathematischen Wissenschaften, Band 134;Huppert, B.,1967

2. A nonembedding theorem for finite groups;Stitzinger, Ernest L.;Proc. Amer. Math. Soc.,1970

3. Errata for two papers of Stitzinger;Stitzinger, Ernest L.;Proc. Amer. Math. Soc.,1972

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

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4. On an embedding of certainp-groups;Israel Journal of Mathematics;1975-03

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