Notes on the average number of Sylow subgroups of finite groups

Jiakuan Lu; Wei Meng; Alexander Moretó; Kaisun Wu

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 4, page 1129-1132
  • ISSN: 0011-4642

Abstract

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We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than 29 4 then G is solvable or G / F ( G ) ≅ A 5 . This generalizes an earlier result by the third author.

How to cite

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Lu, Jiakuan, et al. "Notes on the average number of Sylow subgroups of finite groups." Czechoslovak Mathematical Journal 71.4 (2021): 1129-1132. <http://eudml.org/doc/298097>.

@article{Lu2021,
abstract = {We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than $\frac\{29\}\{4\}$ then $G$ is solvable or $G/F(G)\cong A_5$. This generalizes an earlier result by the third author.},
author = {Lu, Jiakuan, Meng, Wei, Moretó, Alexander, Wu, Kaisun},
journal = {Czechoslovak Mathematical Journal},
keywords = {Fitting subgroup; Sylow subgroup; composition factor},
language = {eng},
number = {4},
pages = {1129-1132},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Notes on the average number of Sylow subgroups of finite groups},
url = {http://eudml.org/doc/298097},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Lu, Jiakuan
AU - Meng, Wei
AU - Moretó, Alexander
AU - Wu, Kaisun
TI - Notes on the average number of Sylow subgroups of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1129
EP - 1132
AB - We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than $\frac{29}{4}$ then $G$ is solvable or $G/F(G)\cong A_5$. This generalizes an earlier result by the third author.
LA - eng
KW - Fitting subgroup; Sylow subgroup; composition factor
UR - http://eudml.org/doc/298097
ER -

References

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  1. Group, GAP, GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra. Version 4.4, Available at http://www.gap-system.org (2005). (2005) 
  2. Guralnick, R. M., Robinson, G. R., 10.1016/j.jalgebra.2005.09.044, J. Algebra 300 (2006), 509-528 addendum ibid 319 2008 1822. (2006) Zbl1100.20045MR2228209DOI10.1016/j.jalgebra.2005.09.044
  3. M. Hall, Jr., 10.1016/0021-8693(67)90076-2, J. Algebra 7 (1967), 363-371. (1967) Zbl0178.02102MR0222159DOI10.1016/0021-8693(67)90076-2
  4. Isaacs, I. M., Loukaki, M., Moretó, A., 10.1007/s11856-013-0013-z, Isr. J. Math. 197 (2013), 55-67. (2013) Zbl1290.20006MR3096606DOI10.1007/s11856-013-0013-z
  5. Moretó, A., 10.1002/mana.201300064, Math. Nachr. 287 (2014), 1183-1185. (2014) Zbl1310.20026MR3231532DOI10.1002/mana.201300064

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