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Character bounds for finite groups of Lie type [PDF]

Acta Mathematica, 2017
We establish new bounds on character values and character ratios for finite groups $G$ of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form $|\chi(g)| \le \chi(1)^
R. Bezrukavnikov, M. Liebeck, A. Shalev, P. Tiep   +3 more
semanticscholar   +11 more sources

Computing in groups of Lie type [PDF]

Mathematics of Computation, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. E. Taylor, Scott H. Murray, Aaron Cohen   +2 more
openaire   +4 more sources

Representations of finite groups of Lie type [PDF]

Bulletin of the American Mathematical Society, 1979
The representation theory of a group G over the field of complex numbers involves two problems: first, the construction of the irreducible representations of G; and second, the problem of expressing each suitably restricted complex valued function on G ...
C. Curtis
semanticscholar   +4 more sources

Generation of finite groups of Lie type [PDF]

Transactions of the American Mathematical Society, 1982
Let p be an odd prime and G a finite group of Lie type in characteristic other than p. Fix an elementary abelian/»-subgroup of Aut(G). It is shown that in most cases G is generated by the centralizers of the maximal subgroups of E.
G. Seitz
semanticscholar   +3 more sources

Covering groups of groups of Lie type [PDF]

Pacific Journal of Mathematics, 1969
John Grover
openaire   +4 more sources

Prime Power Graphs for Groups of Lie Type [PDF]

Journal of Algebra, 2002
Let \(G\)~be a finite simple group of Lie type of characteristic \(p\). Define a graph \(\Gamma(G)\) as follows. The vertices of \(\Gamma(G)\) are the prime powers \(r^a\) that occur as orders of some elements of \(G\), for all primes \(r\not=p\) and integers \(a\).
William M. Kantor, Ákos Seress
openaire   +3 more sources

On the Steinberg presentation for Lie-type groups of type C2

Journal of Algebra, 2002
The article considers abstract groups \(G\) which are generated by subgroups \(A_\alpha \), \(\alpha\in\Phi\), where \(\Phi\) is a root system of one of the types \(A_l\), \(B_l\), \(C_l\), \(D_l\), \(E_l\), \(F_4\), or \(G_2\), and such that \(G\) satisfies (i) if \(\beta\neq-\alpha \) then \([A_\alpha,A_\beta]\leq\langle A_{m\alpha+n\beta}\mid m ...
Claus Müller
openaire   +4 more sources

Sign balance for finite groups of Lie type [PDF]

Linear Algebra and its Applications, 2008
A product formula for the parity generating function of the number of 1's in invertible matrices over Z_2 is given. The computation is based on algebraic tools such as the Bruhat decomposition. The same technique is used to obtain a parity generating function also for symplectic matrices over Z_2.
Yona Cherniavsky, Eli Bagno
openaire   +4 more sources

Growth in finite simple groups of Lie type of bounded rank [PDF]

, 2010
We prove that if L is a finite simple group of Lie type and A a symmetric set of generators of L, then A grows i.e |AAA| > |A|^{1+epsilon} where epsilon depends only on the Lie rank of L, or AAA=L. This implies that for a family of simple groups L of Lie
L. Pyber, E. Szab'o
semanticscholar   +4 more sources

Fusion Systems and Rank $2$ Simple Groups of Lie Type

Forum of Mathematics, Sigma
For any prime p and S a p-group isomorphic to a Sylow p-subgroup of a rank $2$ simple group of Lie type in characteristic p, we determine all saturated fusion systems supported on S up to isomorphism.
Martin van Beek
doaj   +2 more sources