Geodesic
On Numbers which are Orders of Nilpotent Groups Only
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 121-124.

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In [T. W. Müller, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra 300 (2006), 10-15] T. W. Müller characterizes the positive integers n satisfying the property that every group of order n is nilpotent of class bounded by a fixed positive integer c. In this article a different proof of the above result will be given. 
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Russo, Alessio. On Numbers which are Orders of Nilpotent Groups Only. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 121-124. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_1_a6/

[1] L. E. Dickson, Definitions of a group and a field by independent postulates, Trans. Math. Soc., 6 (1905), 198-204. | DOI | MR | Zbl

[2] J. A. Gallian - D. Moulton, When $Z_n$ is the only group of order $n$?, Elem. Math., 48 (1993), 117-119. | fulltext EuDML | MR | Zbl

[3] B. Huppert, Endliche Gruppen I, 2nd edition, Springer, Berlin (1967). | MR

[4] D. Jungnickel, On the uniqueness of the cyclic group of order $n$, Amer. Math. Monthly., 99 (1992), 545-547. | DOI | MR | Zbl

[5] T. W. Müller, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra, 300 (2006), 10-15. | DOI | MR

[6] G. Pazderski, Die Ordnungen, zu denen nur Gruppen mit gegebener Eigenschaft gehören, Arch. Math., 10 (1959), 331-343. | DOI | MR

[7] L. Rédei, Das schiefe Produkt in der Gruppentheorie, Comm. Math. Helv., 20 (1947), 225-264. | fulltext EuDML | DOI | MR

[8] L. Rédei, Die endlichen einstufig nicht nilpotenten Gruppen, Publ. Math. Debrecen, 4 (1956), 303-324. | MR

[9] D. J. S. Robinson, A course in the theory of groups, 2nd edition, Springer, New York (1996). | DOI | MR