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$$(p,q,r)$$-generations and $$nX$$-complementary generations of the sporadic groups $$HS$$ and $$McL$$. (English) Zbl 0874.20017
A group $$G$$ is called $$(l,m,n)$$-generated if it is a quotient of the group which has the presentation $$\langle x,y,z\mid x^l=y^m=z^n=xyz=1\rangle$$. The authors determine all $$(p,q,r)$$-generations ($$p$$, $$q$$, $$r$$ primes) for the sporadic simple Higman-Sims group $$HS$$ and the McLaughlin group $$McL$$. For more related work of the authors see also the article reviewed above (Zbl 0874.20016).

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