Hostname: page-component-7dd5485656-jtdwj Total loading time: 0 Render date: 2025-10-31T13:50:59.661Z Has data issue: false hasContentIssue false
  • English
  • Français

Conjugacy classes of subgroups in p-groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Rolf Brandl
Rolf Brandl
Affiliation:
Mathematisches InstitutAm Hubland 12 D-8700 Würzburg, West Germany
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 set C(G) of conjugacy classes of subgroups of a group G has a natural partial order. We study p-groups G for which C(G) has antichains of prescribed lengths.

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups 20D30: Series and lattices of subgroups 20D60: Arithmetic and combinatorial problems

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 294 - 303
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Brandl, R., ‘The Dilworth number of subgroup lattices’, Arch. Math. 50 (1988), 502–510.CrossRefGoogle Scholar
[2]Hawkes, T. and Isaacs, I.M., ‘On the poset of p-subgroups of a p-solvable group’, J. London Math. Soc. (2) 38 (1988), 77–86.Google Scholar
[3]Hawkes, T., Isaacs, I.M. and Özaydin, M., ‘On the Möbius function of a finite group’, Rocky Mountain J. Math. 19 (1989), 1003–1034.Google Scholar
[4]Huppert, B., Endliche Gruppen 1 (Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar
[5]Landau, E., ‘Über die Klassenzahl der binären quadratischen Formen von negativer Discriminante’, Math. Ann. 56 (1903), 671–676.CrossRefGoogle Scholar