Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A nonembedding theorem for finite groups


Author: Ernest L. Stitzinger
Journal: Proc. Amer. Math. Soc. 25 (1970), 124-126
MSC: Primary 20.25
DOI: https://doi.org/10.1090/S0002-9939-1970-0258936-1
Erratum: Proc. Amer. Math. Soc. 34 (1972), 631.
MathSciNet review: 0258936
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ N$ be the class of nilpotent groups with the following properties: (1) The center of $ N,{Z_ \bot }(N)$ is of prime order. (2) There exists an abelian characteristic subgroup $ A$ of $ N$ such that $ {Z_1}(N) \subset A \subseteq {Z_2}(N)$ where $ {Z_2}(N)$ is the second term in the upper central series of $ N$. The main result shown is the following: $ N \in \mathfrak{X}$, then $ N$ cannot be an invariant subgroup contained in the Frattini subgroup of a finite group.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20.25

Retrieve articles in all journals with MSC: 20.25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0258936-1
Keywords: Frattini subgroup
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society