Search results for "20D06"

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Lie Algebras Generated by Extremal Elements

1999

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.

17B05[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Non-associative algebraAdjoint representationGroup Theory (math.GR)01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Graded Lie algebraCombinatoricsMathematics - Algebraic Geometry0103 physical sciences[MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA]FOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]MathematicsDiscrete mathematicsAlgebra and Number TheorySimple Lie group010102 general mathematics[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]20D06[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Rings and AlgebrasKilling formAffine Lie algebra[ MATH.MATH-RA ] Mathematics [math]/Rings and Algebras [math.RA]Lie conformal algebra[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Adjoint representation of a Lie algebraRings and Algebras (math.RA)17B05; 20D06010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Group TheoryJournal of Algebra
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Finite Groups with Odd Sylow Normalizers

2016

We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups.

Pure mathematicsApplied MathematicsGeneral Mathematics010102 general mathematicsSylow theoremsFoundation (engineering)Group Theory (math.GR)20D06 20D2001 natural sciencesMathematics::Group Theory0103 physical sciencesFOS: Mathematics010307 mathematical physicsRepresentation Theory (math.RT)0101 mathematicsMathematics::Representation TheoryMathematics - Group TheoryMathematics - Representation TheoryMathematics
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