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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): A. Jaikin-Zapirain
Journal: Proc. Amer. Math. Soc. 133 (2005), 2817-2820.
MSC (2000): Primary 20D15; Secondary 17B30
Posted: March 24, 2005
MathSciNet review: 2159757
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Abstract | References | Similar articles | Additional information

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:

1.
Y. Barnea and I. M. Isaacs, Lie algebras with few centralizer dimensions, J. Algebra 259 (2003), 284-299. MR 1953720 (2004a:17005)

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)

4.
M. R. Vaughan-Lee, Breadth and commutator subgroups of $p$-groups, J. Algebra 32 (1974), 278-285. MR 0364436 (51:690)

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Additional Information:

A. Jaikin-Zapirain
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email: andrei.jaikin@uam.es

DOI: 10.1090/S0002-9939-05-07905-0
PII: S 0002-9939(05)07905-0
Keywords: $p$-groups, nilpotent Lie algebras, conjugacy class sizes
Received by editor(s): May 19, 2004
Posted: 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
Copyright of article: Copyright 2005, American Mathematical Society




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