Skip to main content Accessibility help
×
Home
Hostname: page-component-544b6db54f-bkjnw Total loading time: 0.141 Render date: 2021-10-22T08:18:29.856Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS

Published online by Cambridge University Press:  07 February 2012

J. C. BEIDLEMAN*
Affiliation:
Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027, USA (email: clark@ms.uky.edu)
H. HEINEKEN
Affiliation:
Institut für Mathematik, Universität Würzburg, Emil-Fischer-Strasse 30, 97074 Würzburg, Germany (email: heineken@mathematik.uni-wuerzburg.de)
*
For correspondence; e-mail: clark@ms.uky.edu
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the class of solvable groups in which all subnormal subgroups have subnormal normalizers, a class containing many well-known classes of solvable groups. Groups of this class have Fitting length three at most; some other information connected with the Fitting series is given.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Agrawal, R. K., ‘Finite groups where subnormal subgroups permute with all Sylow subgroups’, Proc. Amer. Math. Soc. 47 (1975), 7783.CrossRefGoogle Scholar
[2]Asaad, M., Ballester-Bolinches, A. and Esteban-Romero, R., Products of Finite Groups, Expositions in Mathematics, 53 (W. de Gruyter, Berlin–New York, 2010).Google Scholar
[3]Huppert, B., Endliche Gruppen I (Springer, Berlin–Heidelberg–New York, 1967).Google Scholar
[4]Kegel, O. H., ‘Sylow-Gruppen und Subnormalteiler endlicher Gruppen’, Math. Z. 78 (1962), 205221.CrossRefGoogle Scholar
[5]Maier, R. and Schmid, P., ‘The embedding of quasinormal subgroups in finite groups’, Math. Z. 131 (1973), 269272.CrossRefGoogle Scholar
[6]Robinson, D. J. S., A course in the Theory of Groups, 2 edn, Graduate Texts in Mathematics, 80 (Springer, Berlin–Heidelberg–New York, 1996).CrossRefGoogle Scholar
[7]Schmid, P., ‘Subgroups permutable with all Sylow subgroups’, J. Algebra 207 (1998), 285293.CrossRefGoogle Scholar
You have Access

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *