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On Local Embedding Properties of Injectors of Finite Soluble Groups

Part of: Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Stephanie Reifferscheid
Stephanie Reifferscheid
Affiliation:
Wilhelm-Schickard Institut für Informatik Universität TübingenSand 14, 72076 Tübingen, Germany e-mail: reifferscheid@informatik.uni-tuebingen.de
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Abstract

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In the present paper we consider Fitting classes of finite soluble groups which locally satisfy additional conditions related to the behaviour of their injectors. More precisely, we study Fitting classes 1 ≠⊆such that an-injector of G is, respectively, a normal, (sub)modular, normally embedded, system permutable subgroup of G for all G ∈.

Locally normal Fitting classes were studied before by various authors. Here we prove that some important results—already known for normality—are valid for all of the above mentioned embedding properties. For instance, all these embedding properties behave nicely with respect to the Lockett section. Further, for all of these properties the class of all finite soluble groups G such that an x-injector of G has the corresponding embedding property is not closed under forming normal products, and thus can fail to be a Fitting class.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20F17: Formations of groups, Fitting classes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 23 - 38
Copyright
Copyright © Australian Mathematical Society 2004

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