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PROPERTIES OF SUBGROUPS OF SOLVABLE GROUPS THAT IMPLY THEY ARE NORMALLY EMBEDDED

Published online by Cambridge University Press:  01 May 2003

ARNOLD FELDMAN
ARNOLD FELDMAN
Affiliation:
Franklin and Marshall College, Lancaster, PA 17604-3003, USA e-mail: arny.feldman@fandm.edu
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Abstract

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Recently, Ballester-Bolinches [1 and 2], Pedraza-Aguilera [2] and Perez-Ramos [2] have studied circumstances under which certain injectors and projectors, which are always pronormal, must be normally embedded. In this note we give a scheme for describing a minimal counterexample to a conjecture of the form: a subnormally embedded subgroup with properties $\alpha_1$, $\alpha_2,{\ldots\,},\alpha_{n}$ is normally embedded, where $\alpha_1$, $\alpha_2,{\ldots\,},\alpha_{n}$ satisfy certain conditions. We then show contradictions in certain cases involving finite solvable groups.

Keywords

20D10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 45 - 52
Copyright
2003 Glasgow Mathematical Journal Trust