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\(nX\)-complementary generations of the Rudvalis group \(Ru\). (English) Zbl 1084.20009
Summary: Let \(G\) be a finite group and \(nX\) a conjugacy class of elements of order \(n\) in \(G\). \(G\) is called \(nX\)-complementary generated if, for every \(x\in G-\{1\}\), there is a \(y\in nX\) such that \(G=\langle x,y\rangle\).
J. Moori [in Nova J. Algebra Geom. 2, No. 3, 277-285 (1993; Zbl 0868.20016)] posed the question of finding all positive integers \(n\) such that a given non-Abelian finite simple group \(G\) is \(nX\)-complementary generated. In this paper we answer this question for the sporadic group \(Ru\). In fact, we prove that for any element order \(n\) of the sporadic group \(Ru\), \(Ru\) is \(nX\)-complementary generated if and only if \(n\geq 3\).
Reviewer: Reviewer (Berlin)

20D08 Simple groups: sporadic groups
20F05 Generators, relations, and presentations of groups