On the ranks of Conway group \(Co_1\). (English) Zbl 1083.20014

Summary: Let \(G\) be a finite group and \(X\) a conjugacy class of \(G\). We denote \(\text{rank}(G:X)\) to be the minimum number of elements of \(X\) generating \(G\). In the present paper we investigate the ranks of the Conway group \(Co_1\). Computations are carried out with the aid of computer algebra system GAP [The GAP Group, GAP – Groups, Algorithms and Programming, http://www-gap.dcs.st-and.ac.uk/gap].


20D08 Simple groups: sporadic groups
20F05 Generators, relations, and presentations of groups
20E45 Conjugacy classes for groups
20C40 Computational methods (representations of groups) (MSC2010)


Full Text: DOI


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