Abstract
We generalize the familiar principle of enumeration due to Hall and establish a new principle for the enumeration of subgroups of any p-group G of order pm, based on the following grouptheoretic relation found by the author:
where ℰλ (G) is the number of elementary Abelian subgroups of order pλ in G.
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F. Hall, “A contribution to the theory of groups of prime power order,” Proc. London Math. Soc., (2),36, 29–95 (1933).
M. Hall, The Theory of Groups, Macmillan, New York (1959).
V. N. Shokuev, “Generalizations of Hall's principle of enumeration,” Matem. Zapiski,6, No. 1, 124–143 (1967).
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Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 107–112, January, 1973.
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Shokuev, V.N. The enumeration of subgroups in finite p-groups. Mathematical Notes of the Academy of Sciences of the USSR 13, 64–66 (1973). https://doi.org/10.1007/BF01093632
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DOI: https://doi.org/10.1007/BF01093632