On computing the number of subgroups of a finite Abelian group |
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| Authors: | Thomas Stehling |
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| Institution: | (1) Fachbereich Mathematik der Universität Dortmund, Postfach 500 500, 4600 Dortmund 50, FRG |
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| Abstract: | We consider the numberN
A
(r) of subgroups of orderp
r
ofA, whereA is a finite Abelianp-group of type  =1,2,...,
l
()), i.e. the direct sum of cyclic groups of order ii. Formulas for computingN
A
(r) are well known. Here we derive a recurrence relation forN
A
(r), which enables us to prove a conjecture of P. E. Dyubyuk about congruences betweenN
A
(r) and the Gaussian binomial coefficient
![$$\left {\begin{array}{*{20}c} {l(\alpha ) + r - 1} \\ r \\ \end{array} } \right]$$](/content/m2613713k5u32105/493_2005_Article_BF01305239_TeX2GIFIE1.gif)
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| Keywords: | 05 A 15 20 K 01 |
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