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

Part of: Representation theory of groups Lie algebras and Lie superalgebras Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

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

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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.

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups 20E45: Conjugacy classes 17B30: Solvable, nilpotent (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 2 , October 2006 , pp. 209 - 214
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Barnea, Y. and Isaacs, I. M., ‘Lie algebras with few centralizer dimensions’, J. Algebra 259 (2003), 284–299.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), 49–51.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), 333–345.CrossRefGoogle Scholar
[7]Ishikawa, K., ‘On finite p-groups which have only two conjugacy lengths’, Israel J. Math. 129 (2002), 119–123.Google Scholar
[8]Mann, A., ‘Groups with few class sizes and the centraliser equality subgroup’, Israel J. Math. 142 (2004), 367–380.CrossRefGoogle Scholar