TY - JOUR
ID - 3746
TI - The Validity of a Thompsonâ€™s Problem for PSL(4, 7)
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN -
AU - Khosravi, Behrooz
AU - Kalantarpour, Cyrus
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
Y1 - 2020
PY - 2020
VL - 1
IS - 1
SP - 89
EP - 94
KW - Thompsonâ€™s problem
KW - Characterization
KW - Number of elements of the same order
KW - Projective special linear group
KW - Hall subgroup
KW - NSE
KW - Sporadic groups
KW - Python
DO - 10.22060/ajmc.2019.16174.1022
N2 - Let $pi_e(G)$ be the set of elements orders of $ G$. Also let $ s_n$ be the number of elements of order $n$ in $G $ and ${rm nse}(G)= lbrace s_nmid nin pi_e(G) rbrace $.In this paper we prove that if $ G$ is a group such that ${rm nse}(G)= {rm nse}(rm PSL(4,7)) $, $19bigvert|G|$ and $19^2nmid|G|$, then $ Gcong rm PSL(4,7)$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $rm PSL(4,7)$.
UR - https://ajmc.aut.ac.ir/article_3746.html
L1 - https://ajmc.aut.ac.ir/article_3746_c15795a34e3e77400bdbc8563d65144d.pdf
ER -