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Enumerating subgroups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

R. J. Cook ,
James Wiecold  and
A. G. Wellamson
R. J. Cook
Affiliation:
Department of Pure MathematiocsThe University Sheffield, England
James Wiecold
Affiliation:
Department of Pure MathematicsUniversity CollegeCardiff Wales
A. G. Wellamson
Affiliation:
Haywards Heath CollegeHaywards Heath West Sussex, England
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Abstract

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It is proved that a finite soluble group of order n has at most (n − 1)/(q − 1) maximal subgroups, where q is the smallest prime divisor of n.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 2 , October 1987 , pp. 220 - 223
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Hall, P., ‘A contribution to the theory of groups of prime-power order’, Proc. London Math. Soc. 36 (1933), 29–95.Google Scholar
[2]Neumann, P. M., ‘An enumeration theorem for finite groups’, Quart. J. Math. Oxford Ser. (2) 20 (1969), 395–401.CrossRefGoogle Scholar
[3]Remak, R., ‘Über minimale invariante Untergruppen in der Theorie der endlichen Gruppen’, J. Reine Angew. Math. 162 (1930), 1–16.Google Scholar