Harmonic numbers and finite groups
Rendiconti del Seminario Matematico della Università di Padova, Volume 132 (2014), p. 33-44
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@article{RSMUP_2014__132__33_0,
     author = {Jyoti Baishya, Sekhar and Kumar Das, Ashish},
     title = {Harmonic numbers and finite groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {132},
     year = {2014},
     pages = {33-44},
     zbl = {06379714},
     mrnumber = {3276824},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2014__132__33_0}
}
Jyoti Baishya, Sekhar; Kumar Das, Ashish. Harmonic numbers and finite groups. Rendiconti del Seminario Matematico della Università di Padova, Volume 132 (2014) pp. 33-44. http://www.numdam.org/item/RSMUP_2014__132__33_0/

[1] G. L. Cohen, Numbers whose positive divisors have small integral harmonic mean, Math. Comp., 66 (1997), pp. 883–891. | MR 1397443 | Zbl 0882.11002

[2] A. K. Das, On arithmetic functions of finite groups, Bull. Austral. Math. Soc., 75 (2007), pp. 45–58. | MR 2309547 | Zbl 1126.11003

[3] M. Garcia, On numbers with integral harmonic mean, Amer. Math. Monthly, 61 (1954), pp. 89–96. | MR 59291 | Zbl 0058.27502

[4] T. Goto - S. Shibata, All numbers whose positive divisors have integral harmonic mean up to 300, Math. Comp., 73 (2004), pp. 475–491. | MR 2034133 | Zbl 1094.11005

[5] T. Goto - K. Okeya, All harmonic numbers less than 10 14 , Japan J. Indust. Appl. Math., 24 (2007), pp. 275–288. | MR 2374991 | Zbl 1154.11004

[6] H. J. Kanold, Über das harmonische Mittel der Teiler einer natürlichen Zahl, Math. Ann., 133 (1957), pp. 371–374. | MR 89219 | Zbl 0082.03604

[7] H. Kurzweil - B. Stellmacher, The theory of finite groups, Springer-Verlag, New York, 2004. | MR 2014408 | Zbl 1047.20011

[8] T. Leinster, Perfect numbers and groups, arXiv:math. GR/0104012v1Apr2001.

[9] T. De Medts - M. Tărnăuceanu, Finite groups determined by an inequality of the orders of their subgroups, Bull. Belg. Math. Soc. Simon Stevin, 15 (4) (2008), pp. 699–704. | MR 2475493 | Zbl 1166.20017

[10] T. De Medts - A. Maróti, Perfect numbers and finite groups, Rend. Sem. Mat. Univ. Padova, 129 (2013), pp. 1733. | Numdam | MR 3090628 | Zbl 1280.20026

[11] O. Ore, On the Averages of the Divisors of a Number, Amer. Math. Monthly, 55 (1948), pp. 615–619. | MR 27292 | Zbl 0031.10903

[12] M. W. Short, The Primitive soluble permutation groups of degree less than 256, Lect. Notes in Maths. 1519, Springer-Verlag, Berlin, 1992. | MR 1176516 | Zbl 0752.20001

[13] M. Tărnăuceanu, Finite groups determined by an inequality of the orders of their normal subgroups, Sci. An. Univ. Al.I. Cuza Iasi, Math., 57 (2011) pp. 229–238. | MR 2933379 | Zbl 1240.20035

[14] MathOverflow, http://mathoverflow.net/questions/54851.

[15] The GAP Group, GAP Groups, Algorithms, and Programming, Version 4.6.4, 2013 http://www.gap-system.org).