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$$nX$$-complementary generations of the sporadic group $$He$$. (English) Zbl 1138.20015
Summary: A finite group $$G$$ with conjugacy class $$nX$$ is said to be $$nX$$-complementary generated if, given an arbitrary $$x\in G-\{1\}$$, there is a $$y\in nX$$ such that $$G=\langle x,y\rangle$$. The $$nX$$-complementary generations of the simple groups were first introduced by A. J. Woldar [Commun. Algebra 22, No. 2, 675-685 (1994; Zbl 0806.20020)] to show that every sporadic simple group is $$pX$$-complementary generated for a suitable prime $$p$$. In this paper we investigate all the $$nX$$-complementary generations of the Held group $$He$$ and prove that the group $$He$$ is $$nX$$-complementary generated if and only if $$nX=3B$$ or $$n\geq 4$$.
Reviewer: Reviewer (Berlin)

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