On Numbers which are Orders of Nilpotent Groups Only

Alessio Russo

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 1, page 121-124
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Russo, Alessio. "On Numbers which are Orders of Nilpotent Groups Only." Bollettino dell'Unione Matematica Italiana 5.1 (2012): 121-124. <http://eudml.org/doc/290946>.

@article{Russo2012,
abstract = {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.},
author = {Russo, Alessio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {121-124},
publisher = {Unione Matematica Italiana},
title = {On Numbers which are Orders of Nilpotent Groups Only},
url = {http://eudml.org/doc/290946},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Russo, Alessio
TI - On Numbers which are Orders of Nilpotent Groups Only
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/2//
PB - Unione Matematica Italiana
VL - 5
IS - 1
SP - 121
EP - 124
AB - 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.
LA - eng
UR - http://eudml.org/doc/290946
ER -

References

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  1. DICKSON, L. E., Definitions of a group and a field by independent postulates, Trans. Math. Soc., 6 (1905), 198-204. Zbl36.0207.01MR1500706DOI10.2307/1986298
  2. GALLIAN, J. A. - MOULTON, D., When Z n is the only group of order n ?, Elem. Math., 48 (1993), 117-119. Zbl0829.20035MR1240612
  3. HUPPERT, B., Endliche Gruppen I, 2nd edition, Springer, Berlin (1967). MR224703
  4. JUNGNICKEL, D., On the uniqueness of the cyclic group of order n , Amer. Math. Monthly., 99 (1992), 545-547. Zbl0779.20011MR1166004DOI10.2307/2324062
  5. MÜLLER, T. W., An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra, 300 (2006), 10-15. MR2228629DOI10.1016/j.jalgebra.2005.10.013
  6. PAZDERSKI, G., Die Ordnungen, zu denen nur Gruppen mit gegebener Eigenschaft gehören, Arch. Math., 10 (1959), 331-343. MR114863DOI10.1007/BF01240807
  7. RÉDEI, L., Das schiefe Produkt in der Gruppentheorie, Comm. Math. Helv., 20 (1947), 225-264. MR21933DOI10.1007/BF02568131
  8. RÉDEI, L., Die endlichen einstufig nicht nilpotenten Gruppen, Publ. Math. Debrecen, 4 (1956), 303-324. MR78998
  9. ROBINSON, D. J. S., A course in the theory of groups, 2nd edition, Springer, New York (1996). MR1357169DOI10.1007/978-1-4419-8594-1

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