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Partial Steinberg Modules for Finite Groups of Lie Type
Bulletin of the London Mathematical Society, 1993Let \(G = G_ \phi(q)\) be a universal Chevalley group of type \(A\), \(D\) or \(E\) corresponding to the root system \(\phi\) and defined over the finite field \(F\) of \(q\) elements. Let \(X = X_ \alpha\) be a root subgroup of \(G\) corresponding to a root \(\alpha \in \Phi\); and let \(V\) be a simple \(FG\)-module.
Alperin, J. L., Mason, Geoffrey
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Finite Sylow Subgroups in Simple Locally Finite Groups of Lie Type
Siberian Mathematical Journal, 2005Summary: The main result of the paper is the following Theorem: Let \(S=\{r_0,r_1,\dots,r_n\}\) be a finite nonempty set of primes and let \(L\) be a Lie type of Chevalley groups. Then there exists a locally finite field \(F\) of characteristic \(r_0\) such that Sylow \(r\)-subgroups of the simple group \(L(F)\) of type \(L\) over \(F\) are finite if ...
Kuzucuoğlu, Mahmut, Mazurov, V. D.
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On triangle generation of finite groups of Lie type
Journal of Group Theory, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generic \(2\)-coverings of finite groups of Lie type.
2006Summary: In [J. Algebra 59, 202-221 (1979; Zbl 0409.20033)] it was shown by \textit{R. H. Dye} that in a symplectic group \(G:=\text{Sp}_{2l}(2^f)=\text{Iso}(V,\langle\cdot,\cdot\rangle)\) defined over a finite field of characteristic 2 every element in \(G\) stabilizes a quadratic form of maximal or non-maximal Witt index inducing the bilinear form \(\
BUBBOLONI, DANIELA +2 more
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Invariable generation of finite groups of Lie type
2020A subset of a group invariably generates the group if it generates even when we replace the elements by any of their conjugates. The probability that four randomly selected elements invariably generate S? is bounded away from zero by an absolute constant for all n, but for three elements, the probability tends to zero as n ? ?.
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Modular Representations of Finite Groups of Lie Type
2005Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a
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Character Degrees and Random Walks in Finite Groups of Lie Type
, 2005M. Liebeck, A. Shalev
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Basic sets of Brauer characters of finite groups of Lie type.
, 1991G. Hiss, M. Geck
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