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A note on growth sequences of finite simple groups

Published online by Cambridge University Press:  17 April 2009

Ahmad Erfanian  and
James Wiegold
Ahmad Erfanian
Affiliation:
School of Mathematics, University of Wales, College of Cardiff, Senghennydd Road, Cardiff CF2 4YH, Wales, United Kingdom
James Wiegold
Affiliation:
School of Mathematics, University of Wales, College of Cardiff, Senghennydd Road, Cardiff CF2 4YH, Wales, United Kingdom
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Abstract

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The aim of this paper is to give a new precise formula for h(n, A), where A is a finite non-abelian simple group, h(n, A) is the maximum number such that Ah(n, A) can ke generated by n elements, and n ≥ 2. P. Hall gave a formula for h(n, A) in terms of the Möbius function of the subgroup lattice of A; the new formula involves a concept called cospread associated with that of spread as explained in Brenner and Wiegold (1975).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 495 - 499
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Brenner, J.L. and Wiegold, J., ‘Two generator groups I’, Michigan Math. J. 22 (1975), 53–64.CrossRefGoogle Scholar
[2]Brenner, J.L. and Wiegold, J., ‘Two generator groups II’, Bull. Austral. Math. Soc. 22 (1980), 113–124.CrossRefGoogle Scholar
[3]Brenner, J.L., Guralnick, R.M. and Wiegold, James, ‘Two generator groups III’, Contemp. Math. 33 (1984), 82–89.CrossRefGoogle Scholar
[4]Evans, M.J., ‘A note on two-generator groups’, Rocky Mountain J. Math. 17 (1987), 887–889.CrossRefGoogle Scholar
[5]Hall, P., ‘The Eulerian functions of a group’, Quart. J. Math. Oxford 7 (1936), 134–151.CrossRefGoogle Scholar
[6]Meier, D. and Wiegold, J., ‘Growth sequences of finite groups V’, J. Austral. Math. Soc. Ser. A 31 (1981), 374–375.CrossRefGoogle Scholar
[7]Wiegold, J., ‘Growth sequences of finite groups’, J. Austral. Math. Soc. 17 (1974), 133–141.CrossRefGoogle Scholar
[8]Wiegold, J., ‘Growth sequences of finite groups II’, J. Austral. Math. Soc. 20 (1975), 225–229.CrossRefGoogle Scholar
[9]Wiegold, J., ‘Growth sequences of finite groups III’, J. Austral. Math. Soc. 25 (1978), 142–144.CrossRefGoogle Scholar
[10]Wiegold, J., ‘Growth sequences of finite groups IV’, J. Austral. Math. Soc. 29 (1980), 14–16.CrossRefGoogle Scholar
[11]Wiegold, James and Wilson, J.S., ‘Growth sequences of finitely generated groups’, Arch. Math. 30 (1978), 337–343.CrossRefGoogle Scholar