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The Carter Subgroups of Some Classical Groups
Author(s) -
Previtali A.,
Tamburini M. C.,
Vdovin E. P.
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002558
Subject(s) - mathematics , centralizer and normalizer , sylow theorems , conjugacy class , conjecture , counterexample , simple group , classical group , combinatorics , locally finite group , finite group , unitary state , mathematics subject classification , group (periodic table) , simple (philosophy) , pure mathematics , lie group , philosophy , chemistry , abelian group , organic chemistry , epistemology , political science , law
It is shown that a Carter subgroup of a non‐soluble unitary group can only be the normalizer of a Sylow 2‐subgroup. This result, combined with previous results, implies that no finite simple group can be a minimal counterexample to the conjugacy conjecture of Carter subgroups in a finite group. 2000 Mathematics Subject Classification 20D25, 20D05, 20E07.