Character Degrees and Random Walks in Finite Groups of Lie Type

By Martin W. Liebeck, Aner Shalev. 2005

99 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/050f64f53d6defb29498a5056614ffcab265c0d3

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Citations in the corpus

Representation zeta functions of compact p-adic analytic groups and arithmetic groups (2010, background): “Interesting new phenomena occur when one takes an asymptotic point of view, as illustrated in [37] which focuses on character degrees of finite groups H of Lie type as |H| tends to infinity.”
Word maps, conjugacy classes, and a noncommutative Waring-type theorem (2009, background): “This follows from the discussion in Section 6 of [21] (see Lemma 6.”
Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements (2009, methodology): “(4) Liebeck and Shalev [LS1] have used bounds in the current paper to study probabilistic results about homomorphisms of certain Fuchsian groups into Chevalley groups, and random walks on Chevalley groups [ LS2 ].”
Commutator maps, measure preservation, and T-systems (2007, methodology): “Our constructive proof of Theorem 1.5 applies some powerful recent results on character values and degrees (see [LiSh3, LiSh4, MS, Sh]) to estimate the right hand side of Frobenius formula (1) for speciﬁc (almost all) elements g ∈ G , showing that the main contribution comes from the trivial charact”
Base sizes for simple groups and a conjecture of Cameron (2009, methodology): “If G is a classical group with natural module of dimension greater than 15 then a theorem of Liebeck and Shalev [ 49, Theorem 1.11 ] establishes the conjecture with a best possible constant c! = 3. By considering the remaining classical groups of small rank we prove the following theorem.”
Base size, metric dimension and other invariants of groups and graphs (2011, background): “Progress towards this conjecture has been made by Gluck and various coauthors [59, 60], by Liebeck and Shalev [76], and in the (unpublished) PhD thesis of Benbenishty [13]; see [77] for further details.”
On base sizes for actions of finite classical groups (2007, background): “Note that in summing over all conjugacy classes, the definition of ηG(t) in [22] differs slightly from ours.”