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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
Software:
GAP
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References:
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