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Centralizer sizes and nilpotency class in Lie algebras and finite  -groups
Author:
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: 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  -groups.
- 1.
Yiftach
Barnea and I.
M. Isaacs, Lie algebras with few centralizer dimensions, J.
Algebra 259 (2003), no. 1, 284–299. MR 1953720
(2004a:17005), http://dx.doi.org/10.1016/S0021-8693(02)00558-6
- 2.
Kenta
Ishikawa, On finite 𝑝-groups which have only two conjugacy
lengths, Israel J. Math. 129 (2002), 119–123.
MR
1910937 (2004b:20032), http://dx.doi.org/10.1007/BF02773158
- 3.
Noboru
Itô, 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)
- 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
 -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
 -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:
http://dx.doi.org/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
Article copyright:
© Copyright 2005 American Mathematical Society
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