TY - JOUR
ID - 17196
TI - A characterization of the Suzuki group Sz(2^9) by the set of the number of elements with the same order
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - Parvizi Mosaed, Hosein
AU - Deneshkhah, Ashraf
AU - Alavi, Seyed Hassan
AD - Alvand Institute of Higher Education, Hamedan, Iran
AD - Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
Y1 - 1400
PY - 1400
VL - 11
IS - 4
SP - 679
EP - 685
KW - Finite simple group
KW - Suzuki group
KW - Element order
KW - Prime graph
DO - 10.22055/jamm.2021.38473.1961
N2 - Let G be a group, and let nse(G) be the set of the number of elements with the same order in group G. In this paper, we prove that if G is a group and Sz(2^9) is the Suzuki simple group such that nse(G) = nse(Sz(2^9)), then G is isomorphic to the Suzuki simple group Sz(2^9). In other words, we prove that the simple Suzuki group Sz(2^9) is uniquely determined by its set of the number of elements with the same order. Consequently, Thompsonâ€™s problem is true for the Suzuki simple group Sz(2^9 ).
UR - https://jamm.scu.ac.ir/article_17196.html
L1 - https://jamm.scu.ac.ir/article_17196_46dbbeb39a67106f317d13188938f5db.pdf
ER -