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The efficiency of PSL(2, p)3 and other direct products of groups

  • C. M. Campbell (a1), I. Miyamoto (a2), E. F. Robertson (a3) and P. D. Williams (a4)

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A finite group G is efficient if it has a presentation on n generators and n + m relations, where m is the minimal number of generators of the Schur multiplier M (G)of G. The deficiency of a presentation of G is r–n, where r is the number of relations and n the number of generators. The deficiency of G, def G, is the minimum deficiency over all finite presentations of G. Thus a group is efficient if def G = m. Both the problem of efficiency and the converse problem of inefficiency have received considerable attention recently; see for example [1], [3], [14] and [15].

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References

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The efficiency of PSL(2, p)3 and other direct products of groups

  • C. M. Campbell (a1), I. Miyamoto (a2), E. F. Robertson (a3) and P. D. Williams (a4)

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