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Referenza completa

Russo, Alessio:
On Numbers which are Orders of Nilpotent Groups Only
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.1, p. 121-124, (English)
pdf (230 Kb), djvu (46 Kb). | MR 2919652 | Zbl 1251.20026

Sunto

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.
Referenze Bibliografiche
[1] L. E. DICKSON, Definitions of a group and a field by independent postulates, Trans. Math. Soc., 6 (1905), 198-204. | fulltext (doi) | MR 1500706 | Zbl 36.0207.01
[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 1240612 | Zbl 0829.20035
[3] B. HUPPERT, Endliche Gruppen I, 2nd edition, Springer, Berlin (1967). | MR 224703
[4] D. JUNGNICKEL, On the uniqueness of the cyclic group of order $n$, Amer. Math. Monthly., 99 (1992), 545-547. | fulltext (doi) | MR 1166004 | Zbl 0779.20011
[5] T. W. MÜLLER, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra, 300 (2006), 10-15. | fulltext (doi) | MR 2228629
[6] G. PAZDERSKI, Die Ordnungen, zu denen nur Gruppen mit gegebener Eigenschaft gehören, Arch. Math., 10 (1959), 331-343. | fulltext (doi) | MR 114863
[7] L. RÉDEI, Das schiefe Produkt in der Gruppentheorie, Comm. Math. Helv., 20 (1947), 225-264. | fulltext EuDML | fulltext (doi) | MR 21933
[8] L. RÉDEI, Die endlichen einstufig nicht nilpotenten Gruppen, Publ. Math. Debrecen, 4 (1956), 303-324. | MR 78998
[9] D. J. S. ROBINSON, A course in the theory of groups, 2nd edition, Springer, New York (1996). | fulltext (doi) | MR 1357169

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