Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T06:24:10.664Z Has data issue: false hasContentIssue false

Isoclinisms and covering groups

Published online by Cambridge University Press:  17 April 2009

Michael R. Jones
Affiliation:
199 Elm Drive, Ty-Sign Estate, Pontymister, Risca, Monmouthshire, UK;
James Wiegold
Affiliation:
Department of Pure Mathematics, University College, Cardiff, Wales.
Rights & Permissions [Opens in a new window]

Abstract

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

The article examines the connection between the concepts of isoclinism and covering groups for finite groups. The main result is that all covering groups for a given finite group are mutually isoclinic. The converse is false.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Gaschütz, W., Neubüser, J. und Yen, Ti, “Über den Multiplikator von p–Gruppen”, Math. Z. 100 (1967), 9396.CrossRefGoogle Scholar
[2]Hall, P., “The classification of prime-power groups”, J. reine angew. Math. 182 (1940), 130141.CrossRefGoogle Scholar
[3]Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften, Band 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[4]Neumann, B.H., “Groups with finite classes of conjugate subgroups”, Math. Z. 63 (1955), 7696.CrossRefGoogle Scholar
[5]Schur, J., “Über die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen”, J. reine angew. Math. 127 (1904), 2050.Google Scholar
[6]Schur, J., “Untersuchungen über die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen”, J. reine angew. Math. 132 (1907), 85137.Google Scholar
[7]Wiegold, James, “The derived groups of groups with boundedly finite conjugacy classes”, (MSc thesis, University of Manchester, 1955).Google Scholar