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On the probability of generating a minimal d-generated group

Part of: Probabilistic methods in group theory Permutation groups

Published online by Cambridge University Press:  09 April 2009

F. Dalla Volta ,
A. Lucchini  and
F. Morini
F. Dalla Volta
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano - Bicocca, Via Bicocca Degli Arcimboldi 8, 20126 Milano, Italy
A. Lucchini
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano - Bicocca, Via Bicocca Degli Arcimboldi 8, 20126 Milano, Italy
F. Morini
Affiliation:
Dipartimento di Matematica, Università di Brescia, Via Valotti 9, 25133 Brescia, Italy
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Abstract

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We consider finite groups with the property that any proper factor can be generated by a smaller number of elements than the group itself. We study some problems related with the probability of generating these groups with a given number of elements.

MSC classification

Secondary: 20B05: General theory for finite groups 20P05: Probabilistic methods in group theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 177 - 186
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Aschbacher, M. and Guralnick, R., ‘Some applications of the first cohomology group’, J. Algebra 90 (1984), 446–460.CrossRefGoogle Scholar
[2]Volta, F. Dalla and Lucchini, A., ‘Finite groups that need more generators than any proper quotient’, J. Austral. Math. Soc. Ser. A 64 (1998), 82–91.CrossRefGoogle Scholar
[3]Volta, F. Dalla and Lucchini, A., ‘The smallest group with non zero presentation rank’, J. Group Theory 2 (1999), 147–155.CrossRefGoogle Scholar
[4]Gaschütz, W., ‘Zu einem von B. H. und H. Neumann gestellten Problem’, Math. Nachr. 14 (1955), 249–252.CrossRefGoogle Scholar
[5]Gruenberg, K. W. and Roggenkamp, K. W., ‘Decomposition of the relation modules of a finite group’, J. London Math. Soc. (2) 12 (1976), 262–266.CrossRefGoogle Scholar
[6]Kantor, W. and Lubotzky, A., ‘The probability of generating a finite classical group’, Geom. Dedicata 36 (1990), 67–87.CrossRefGoogle Scholar
[7]Lucchini, A., ‘On groups with d-generators subgroups of coprime index’, Comm. Algebra 28 (2000), 1875–1880.CrossRefGoogle Scholar
[8]Lucchini, A. and Menegazzo, F., ‘Generators for finite groups with a unique minimal normal subgroup’, Rend. Sem. Mat. Univ. Padova 98 (1997), 173–191.Google Scholar
[9]Lucchini, A. and Morini, F., ‘On the probability of generating finite groups with a unique minimal normal subgroup’, Pacific. J. Math. to appear.Google Scholar
[10]Pak, I., ‘On the probability of generating a finite group’, preprint, 2000.Google Scholar