A generalization of the diameter bound of Liebeck and Shalev for finite simple groups

Products of conjugacy classes in simple algebraic groups in terms of diagrams

“…A normal subset of a group G is defined to be a non-empty union of conjugacy classes in G. By a result of Liebeck and Shalev [17,Theorem 1.1], there is a universal constant c such that whenever N is a non-central normal subset in a non-abelian finite simple group G then N k = G for any integer k at least c • (log 2 |G|/ log 2 |N |). This was generalized by Maróti and Pyber in [21,Theorem 1.2], where they prove that there exists a universal constant c such that if N 1 , . .…”

“…The methods used in the context of Chevalley groups give explicit constants for the upper bounds on the (extended) covering numbers which are missing in [17,Theorem 1.1] and [21,Theorem 1.2]. On the other hand the results in [17,21] take into account the size of the normal subsets and should have analogous statements for Chevalley groups.…”

“…The methods used in the context of Chevalley groups give explicit constants for the upper bounds on the (extended) covering numbers which are missing in [17,Theorem 1.1] and [21,Theorem 1.2]. On the other hand the results in [17,21] take into account the size of the normal subsets and should have analogous statements for Chevalley groups. Bridging the two types of results should entail an analysis of simple algebraic groups over algebraically closed fields which are easier to deal with than finite simple groups of Lie type or Chevalley groups over arbitrary fields, yet resembles these type of groups closely through the BN-pair structure.…”