On the number of isomorphism classes of derived subgroups

Leyli Jafari Taghvasani; Soran Marzang; Mohammad Zarrin

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 3, page 665-670
  • ISSN: 0011-4642

Abstract

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We show that a finite nonabelian characteristically simple group G satisfies n = | π ( G ) | + 2 if and only if G ≅ A 5 , where n is the number of isomorphism classes of derived subgroups of G and π ( G ) is the set of prime divisors of the group G . Also, we give a negative answer to a question raised in M. Zarrin (2014).

How to cite

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Taghvasani, Leyli Jafari, Marzang, Soran, and Zarrin, Mohammad. "On the number of isomorphism classes of derived subgroups." Czechoslovak Mathematical Journal 69.3 (2019): 665-670. <http://eudml.org/doc/294720>.

@article{Taghvasani2019,
abstract = {We show that a finite nonabelian characteristically simple group $G$ satisfies $n=|\pi (G)|+2$ if and only if $G\cong A_5$, where $n$ is the number of isomorphism classes of derived subgroups of $G$ and $\pi (G)$ is the set of prime divisors of the group $G$. Also, we give a negative answer to a question raised in M. Zarrin (2014).},
author = {Taghvasani, Leyli Jafari, Marzang, Soran, Zarrin, Mohammad},
journal = {Czechoslovak Mathematical Journal},
keywords = {derived subgroup; simple group},
language = {eng},
number = {3},
pages = {665-670},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the number of isomorphism classes of derived subgroups},
url = {http://eudml.org/doc/294720},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Taghvasani, Leyli Jafari
AU - Marzang, Soran
AU - Zarrin, Mohammad
TI - On the number of isomorphism classes of derived subgroups
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 3
SP - 665
EP - 670
AB - We show that a finite nonabelian characteristically simple group $G$ satisfies $n=|\pi (G)|+2$ if and only if $G\cong A_5$, where $n$ is the number of isomorphism classes of derived subgroups of $G$ and $\pi (G)$ is the set of prime divisors of the group $G$. Also, we give a negative answer to a question raised in M. Zarrin (2014).
LA - eng
KW - derived subgroup; simple group
UR - http://eudml.org/doc/294720
ER -

References

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  8. Longobardi, P., Maj, M., Robinson, D. J. S., 10.1016/j.jalgebra.2013.06.036, J. Algebra 393 (2013), 102-119. (2013) Zbl1294.20049MR3090061DOI10.1016/j.jalgebra.2013.06.036
  9. Longobardi, P., Maj, M., Robinson, D. J. S., Smith, H., 10.1017/S0017089512000821, Glasg. Math. J. 55 (2013), 655-668. (2013) Zbl1287.20046MR3084668DOI10.1017/S0017089512000821
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