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April 2002 A remark on local-global principles for conjugacy classes
Yuval Z. Flicker
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Ark. Mat. 40(1): 47-53 (April 2002). DOI: 10.1007/BF02384501

Abstract

A local-global principle is shown to hold for all conjugacy classes of any inner form of GL(n), SL(n), U(n), SU(n), and for all semisimple conjugacy classes in any inner form of Sp(n), over fields k with vcd(k)≤1. Over number fields such a principle is known to hold for any inner form of GL(n) and U(n), and for the split forms of Sp(n), O(n), as well as for SL(p) but not for SL(n), n non-prime. The principle holds for all conjugacy classes in any inner form of GL(n), but not even for semisimple conjugacy classes in Sp(n), over fields k with vcd(k)≤2. The principle for conjugacy classes is related to that for centralizers.

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Yuval Z. Flicker. "A remark on local-global principles for conjugacy classes." Ark. Mat. 40 (1) 47 - 53, April 2002. https://doi.org/10.1007/BF02384501

Information

Received: 4 September 2000; Revised: 10 October 2000; Published: April 2002
First available in Project Euclid: 31 January 2017

zbMATH: 1075.14505
MathSciNet: MR1948885
Digital Object Identifier: 10.1007/BF02384501

Rights: 2002 © Institut Mittag-Leffler

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