Perfect numbers and finite groups

Tom De Medts; Attila Maróti

Rendiconti del Seminario Matematico della Università di Padova (2013)

  • Volume: 129, page 17-34
  • ISSN: 0041-8994

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De Medts, Tom, and Maróti, Attila. "Perfect numbers and finite groups." Rendiconti del Seminario Matematico della Università di Padova 129 (2013): 17-34. <http://eudml.org/doc/275141>.

@article{DeMedts2013,
author = {De Medts, Tom, Maróti, Attila},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {perfect numbers; finite groups; Leinster groups; orders of normal subgroups; numbers of subgroups},
language = {eng},
pages = {17-34},
publisher = {Seminario Matematico of the University of Padua},
title = {Perfect numbers and finite groups},
url = {http://eudml.org/doc/275141},
volume = {129},
year = {2013},
}

TY - JOUR
AU - De Medts, Tom
AU - Maróti, Attila
TI - Perfect numbers and finite groups
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2013
PB - Seminario Matematico of the University of Padua
VL - 129
SP - 17
EP - 34
LA - eng
KW - perfect numbers; finite groups; Leinster groups; orders of normal subgroups; numbers of subgroups
UR - http://eudml.org/doc/275141
ER -

References

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  1. [1] C. W. Anderson, The solution of Σ ( n ) = σ ( n ) / n = a / b , Φ ( n ) = ϕ ( n ) / n = a / b and some related considerations, unpublished manuscript (1974). 
  2. [2] T. De Medts, Recovering n from σ ( n ) / n , MathOverflow, http://mathoverflow.net/questions/56376. 
  3. [3] T. De Medts - M. Tărnăuceanu, Finite groups determined by an inequality of the orders of their subgroups, Bull. Belg. Math. Soc. Simon Stevin 15, no. 4 (2008), pp. 699–704. Zbl1166.20017MR2475493
  4. [4] B. Huppert, Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin, New York, 1967. MR224703
  5. [5] T. Leinster, Perfect numbers and groups, arXiv:math/0104012. Zbl1273.18009
  6. [6] T. Leinster, Is there an odd-order group whose order is the sum of the orders of the proper normal subgroups?, Math. Overflow, http://mathoverflow.net/questions/54851. 
  7. [7] W. A. Stein et. al., Sage Mathematics Software (Version 4.6.1), The Sage Development Team, 2011, http://www.sagemath.org. 
  8. [8] W. G. Stanton - J. A. Holdener, Abundancy outlaws of the form ( σ ( N ) + t ) / N , J. Integer Sequences 10 (2007), Article 09.7.6. Zbl1174.11005MR2346095
  9. [9] http://java.ugent.be/~tdemedts/leinster. 

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