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Centralizer sizes and nilpotency class in Lie algebras and finite $p$-groups

Author: A. Jaikin-Zapirain
Journal: Proc. Amer. Math. Soc. 133 (2005), 2817-2820
MSC (2000): Primary 20D15; Secondary 17B30
Published electronically: March 24, 2005
MathSciNet review: 2159757
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Abstract: In this work we solve a conjecture of Y. Barnea and M. Isaacs about centralizer sizes and the nilpotency class in nilpotent finite-dimensional Lie algebras and finite $p$-groups.

References [Enhancements On Off] (What's this?)

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  • 2. K. Ishikawa, On finite $p$-groups which have only two conjugacy lengths, Israel J. Math. 129 (2002), 119-123. MR 1910937 (2004b:20032)
  • 3. N. Ito, On finite groups with given conjugate types. I, Nagoya Math. J. 6 (1953), 17-28. MR 0061597 (15:851c)
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Additional Information

A. Jaikin-Zapirain
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Keywords: $p$-groups, nilpotent Lie algebras, conjugacy class sizes
Received by editor(s): May 19, 2004
Published electronically: March 24, 2005
Additional Notes: This work was partially supported by the MCYT Grants BFM2001-0201, BFM2001-0180, FEDER and the Ramón y Cajal Program.
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2005 American Mathematical Society

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