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Some applications of the Eulerian functions of a finite group

Published online by Cambridge University Press:  09 April 2009

G. E. Wall
G. E. Wall
Affiliation:
University of Sydney
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This paper is chiefly concerned with inequalities for the numbers of subgroups of a finite p-group. The following are typical results. Let G be a p-group of order pa, and let nG(pk) denote the number of subgroups of G of order pk.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 1 , April 1961 , pp. 35 - 59
Copyright
Copyright © Australian Mathematical Society 1961

References

[1]Barnes, D. W., Lattice embeddings of prime power group, D. Phil. thesis, Oxford University (1959).Google Scholar
[2]Delsarte, P., Fonctions de Möbius sur les groupes abéliens finis, Ann. of Math. (2) 49 (1948), 600–609.CrossRefGoogle Scholar
[3]Gaschütz, W., Die Eulersche Funktion endlicher auflösbarer Gruppen, Illinois J. Maths. 3 (1959), 469–476.Google Scholar
[4]Hall, P., The Eulerian functions of a group, Quart. J. Maths. (Oxford Series) 7 (1936), 134–151.CrossRefGoogle Scholar
[5]Hall, P., A contribution to the theory of groups of prime-power order, Proc. London Math. Soc. (2) 36 (1933), 29–95.Google Scholar
[6]Kinosita, Y., On the enumeration of certain subgroups of a p-group, J. Osaka Inst. Sci. Tech. Part I 1 (1949), 13–20.Google Scholar
[7]Lazard, M., Sur les groupes nilpotents et les anneaux de Lie, Ann. Sc. de l'École Normale Supérieure 71 (1954), 101–190, (theorem 4.6, p. 176).CrossRefGoogle Scholar
[8]Suzuki, M., Structure of a group and the structure of its lattice of subgroups, Springer (1956).CrossRefGoogle Scholar
[9]Weisner, L., Abstract theory of inversion of finite series, Trans. Amer. Math. Soc. 38 (1935), 474–484.CrossRefGoogle Scholar
[10]Yeh, Y., On prime power abelian groups, Bull. Amer. Math. Soc. 54 (1948), 323–327.CrossRefGoogle Scholar
[11]Zassenhaus, H., The theory of groups, Chelsea (1949).Google Scholar
[12]Kemhadze, Š. S., Soobščeniya Akad. Nauk Gruzin S.S.R. 11 (1950), 607–611.Google Scholar