Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T07:50:01.006Z Has data issue: false hasContentIssue false

Elements of minimal breadth in finite p-groups and lie algebras

Published online by Cambridge University Press:  09 April 2009

Avinoam Mann
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel, e-mail: [email protected]
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.

Let G be a finite p-group, and let M(G) be the subgroup generated by the non-central conjugacy classes of G of minimal size. We prove that this subgroup has class at most 3. A similar result is noted for nilpotent Lie algebras.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Barnea, Y. and Isaacs, I. M., ‘Lie algebras with few centralizer dimensions’, J. Algebra 259 (2003), 284299.CrossRefGoogle Scholar
[2]Bender, H. and Glauberman, G., Local analysis for the odd order theorem (Cambridge University Press, Cambridge, 1994).Google Scholar
[3]Blackburn, N. and Huppert, B., Finite groups III (Springer, Berlin, 1982).Google Scholar
[4]Cossey, J. and Hawkes, T. O., ‘Sets of p-powers as conjugacy class sizes’, Proc. Amer. Math. Soc. 128 (2000), 4951.CrossRefGoogle Scholar
[5]Hall, M., The theory of groups (Macmillan, New York, 1959).Google Scholar
[6]Ishikawa, K., ‘Finite p-groups up to isoclinism, which have only two conjugacy lengths’, J. Algebra 220 (1999), 333345.CrossRefGoogle Scholar
[7]Ishikawa, K., ‘On finite p-groups which have only two conjugacy lengths’, Israel J. Math. 129 (2002), 119123.Google Scholar
[8]Mann, A., ‘Groups with few class sizes and the centraliser equality subgroup’, Israel J. Math. 142 (2004), 367380.CrossRefGoogle Scholar