Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-pgkvd Total loading time: 0.305 Render date: 2022-08-17T16:47:26.706Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Unfaithful minimal Heilbronn characters of L2(q)

Published online by Cambridge University Press:  21 November 2012

Hy Ginsberg*
Affiliation:
Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington, VT 05401, USA

Abstract

When a minimal Heilbronn character θ is unfaithful on a Sylow p-subgroup P of a finite group G, we know that G is quasi-simple, p is odd, P is cyclic, NG(P) is maximal and either NG(P) is the unique maximal subgroup containing Ω1(P) or G/Z(G) ≅ L2(q) for q an odd prime with p dividing q − 1. In this paper we examine the exceptional case, where G/Z(G) ≅ L2(q), explicitly constructing unfaithful minimal Heilbronn characters from the non-principal irreducible characters of G.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Dornhoff, L., Group representation theory, Part A, Pure and Applied Mathematics, Volume 7 (Marcel Dekker, New York, 1971).Google Scholar
2.Foote, R., Sylow 2-subgroups of Galois groups arising as minimal counterexamples to Artin's conjecture, Commun. Alg. 25(2) (1997), 607616.CrossRefGoogle Scholar
3.Ginsberg, H., Unfaithful Heilbronn characters of finite groups, J. Alg. 331 (2011), 466481.CrossRefGoogle Scholar
4.Gorenstein, D., Lyons, R. and Solomon, R., Almost simple K-groups, in The classification of the finite simple groups, Number 3, Mathematical Surveys and Monographs, Volume 40.3, Part I, Chapter A (American Mathematical Society, Providence, RI, 1998).Google Scholar

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@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 saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved 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.

Unfaithful minimal Heilbronn characters of L2(q)
Available formats
×

Save article to Dropbox

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Unfaithful minimal Heilbronn characters of L2(q)
Available formats
×

Save article to Google Drive

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Unfaithful minimal Heilbronn characters of L2(q)
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? *