When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently

Claudia A. Spiro-Silverman

Acta Arithmetica (1992)

  • Volume: 61, Issue: 1, page 1-12
  • ISSN: 0065-1036

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Claudia A. Spiro-Silverman. "When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently." Acta Arithmetica 61.1 (1992): 1-12. <http://eudml.org/doc/206449>.

@article{ClaudiaA1992,
author = {Claudia A. Spiro-Silverman},
journal = {Acta Arithmetica},
keywords = {group-counting; squarefree order; lower bound; finite groups; number of non-isomorphic groups; asymptotic results},
language = {eng},
number = {1},
pages = {1-12},
title = {When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently},
url = {http://eudml.org/doc/206449},
volume = {61},
year = {1992},
}

TY - JOUR
AU - Claudia A. Spiro-Silverman
TI - When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 1
SP - 1
EP - 12
LA - eng
KW - group-counting; squarefree order; lower bound; finite groups; number of non-isomorphic groups; asymptotic results
UR - http://eudml.org/doc/206449
ER -

References

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  1. [1] P. Erdős, Some asymptotic formulas in number theory, J. Indian Math. Soc. 12 (1948), 75-78. Zbl0041.36807
  2. [2] P. Erdős, M. R. Murty, and V. K. Murty, On the enumeration of finite groups, J. Number Theory 25 (1987), 360-378. Zbl0612.10038
  3. [3] H. Halberstam and H.-E. Richert, Sieve Methods, London Math. Soc. Monographs 4, Academic Press, London 1974. Zbl0298.10026
  4. [4] H. Halberstam and K. F. Roth, Sequences, Springer, New York 1983. 
  5. [5] O. Hölder, Die Gruppen mit quadratfreier Ordnungszahl, Nach. Königl. Gessell. der Wiss. Göttingen Math.-Phys. Kl. 1895, 211-229. Zbl26.0162.01
  6. [6] Yu. V. Linnik, On the least prime in an arithmetic progression. II. The Deuring-Heilbronn phenomenon, Mat. Sb. (N.S.) 15 (57) (1944), 347-368. Zbl0063.03585
  7. [7] M.-G. Lu, The asymptotic formula for F₂(x), Sci. Sinica Ser. A 30 (1987), 262-278. 
  8. [8] M. R. Murty and V. K. Murty, On the number of groups of a given order, J. Number Theory 18 (1984), 178-191. Zbl0531.10047
  9. [9] K. K. Norton, On the number of restricted prime factors of an integer. I, Illinois J. Math. 20 (1976), 681-705. Zbl0329.10035
  10. [10] C. A. Spiro, The probability that the number of groups of squarefree order is two more than a fixed prime, Proc. London Math. Soc. 60 (1990), 444-470. Zbl0707.11066
  11. [11] T. Szele, Über die endlichen Ordnungszahlen, zu denen nur eine Gruppe gehört, Comment. Math. Helv. 20 (1947), 265-267. Zbl0034.30502
  12. [12] J. Szép, On finite groups which are necessarily commutative, Comment. Math. Helv., 223-224. Zbl0035.01502

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