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Products of conjugacy classes in Chevalley groups over local rings

Author(s): N. Gordeev; J. Saxl
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 2.
Journal: St. Petersburg Math. J. 17 (2006), 285-293.
MSC (2000): Primary 14L15, 14L17, 20G35
Posted: February 10, 2006
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Abstract: Estimates of extended covering numbers are obtained for Chevalley groups over local rings.

References:

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E. Abe, Chevalley groups over local rings, Tôhoku Math. J. (2) 21 (1969), 474-494. MR 0258837 (41:3483)

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A. Borel, Linear algebraic groups, 2nd ed., Grad. Texts in Math., vol. 126, Springer-Verlag, New York, 1991. MR 1102012 (92d:20001)

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N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitres IV, V, VI, Actualités Sci. Indust., No. 1337, Hermann, Paris, 1968. MR 0240238 (39:1590)

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-, Commutative algebra. Chapters 1-7, Springer-Verlag, Berlin, 1998. MR 1727221 (2001g:13001)

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E. W. Ellers and N. Gordeev, Gauss decomposition with prescribed semisimple part in Chevalley groups. I, II, III, Comm. Algebra 22 (1994), 5935-5950; 23 (1995), 3085-3098; 24 (1996), 4447-4475. MR 1298758 (95m:20052); MR 1332168 (96f:20064); MR 1421200 (98a:20048)

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-, On the conjectures of J. Thompson and O. Ore, Trans. Amer. Math. Soc. 350 (1998), 3657-3671. MR 1422600 (98k:20022)

[GS1]
N. Gordeev and J. Saxl, Products of conjugacy classes in Chevalley groups. I. Extended covering numbers, Israel J. Math. 130 (2002), 207-248. MR 1919378 (2003e:20050)

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-, Products of conjugacy classes in Chevalley groups. II. Covering and generation, Israel J. Math. 130 (2002), 249-258. MR 1919379 (2003e:20051)

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R. Steinberg, Lectures on Chevalley groups, Yale Univ., New Haven, Conn., 1968. MR 0466335 (57:6215)

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Additional Information:

N. Gordeev
Affiliation: Department of Mathematics, Russian State Pedagogical University, Moika 48, St. Petersburg 191186, Russia
Email: nickgordeev@mail.ru

J. Saxl
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
Email: J.Saxl@dpmms.cam.ac.uk

DOI: 10.1090/S1061-0022-06-00904-6
PII: S 1061-0022(06)00904-6
Keywords: Products of conjugacy classes, Chevalley groups
Received by editor(s): 20/MAY/2004
Posted: February 10, 2006
Additional Notes: The first author was supported by EPSRC (grant GR/R79081/01), by Russian Ministry of Education (grant E02--1.0--15), by RTF Network (grant HPRN--CT--2002--00287), and by RFBR (grant no. 03--01--00349).
Copyright of article: Copyright 2006, American Mathematical Society

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