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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)

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