An element g in a finite group G is called a vanishing element if there exists some irreducible complex character x of G such that y(p)=0.Denote by Vo(G)the set of orders of vanishing elements of G,and we prove that G...An element g in a finite group G is called a vanishing element if there exists some irreducible complex character x of G such that y(p)=0.Denote by Vo(G)the set of orders of vanishing elements of G,and we prove that G≌PSL(2,q)if and only if|G|=|PSL(2,q)\and Vo(G)=Vo(PSL(2,q)),where g≥4 is a prime power.展开更多
The authors show that linear simple groups L_2(q) with q ∈ {17, 27, 29} can be uniquely determined by nse(L_2(q)), which is the set of numbers of elements with the same order.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11301218)the Nature Science Fund of Shandong Province(Grant No.ZR2019MA044)the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing(No.2018QZJ04).
文摘An element g in a finite group G is called a vanishing element if there exists some irreducible complex character x of G such that y(p)=0.Denote by Vo(G)the set of orders of vanishing elements of G,and we prove that G≌PSL(2,q)if and only if|G|=|PSL(2,q)\and Vo(G)=Vo(PSL(2,q)),where g≥4 is a prime power.
基金supported by the National Natural Science Foundation of China(Nos.11301218,11301219)the Natural Science Foundation of Shandong Province(No.ZR2014AM020)University of Jinan Research Funds for Doctors(Nos.XBS1335,XBS1336)
文摘The authors show that linear simple groups L_2(q) with q ∈ {17, 27, 29} can be uniquely determined by nse(L_2(q)), which is the set of numbers of elements with the same order.
