فهرست مطالب • Volume:1 Issue:3, 2012
• تاریخ انتشار: 1391/04/06
• تعداد عناوین: 7
|
• هونگ پ تنگ، توماس پ ویکفیلد صفحه 1
• محمدمهدی نصرآبادی، علی غلامیان صفحه 11
• علیرضا خلیلی، سیدصادق صالحی امیری صفحه 15
• چانگون لی، ایکسون لان یی صفحه 21
• هانیه میرابراهیمی، بهروز مشایخی صفحه 33
• فرانچسکو د جیووانی، کاترین رینون صفحه 39
• سیدصادق صالحی امیری، ابوالفضل تهرانیان، علیرضا خلیلی، علی ایرانمنش صفحه 51
|
• Hung P. Tong, Viet, Thomas P. Wakefield Page 1
Let \$G\$ be a finite group and let \$text{cd}(G)\$ be the set of all complex irreducible character degrees of \$G\$. B. Huppert conjectured that if \$H\$ is a finite nonabelian simple group such that \$text{cd}(G) =text{cd}(H)\$, then \$Gcong H times A\$, where \$A\$ is an abelian group. In this paper, we verify the conjecture for \$rm{F_4(2)}.\$
Keywords: Character degrees, Simple groups, Huppert's Conjecture
• Mohammad Mehdi Nasrabadi, Ali Gholamian Page 11
Let \$G\$ be a group and \$A = Aut(G)\$ be the group of automorphisms of \$G\$. Then the element \$[g,alpha] = g^{-1}alpha(g)\$ is an au- tocommutator of \$gin G\$ and \$alphain A\$. Also, the autocommutator subgroup of G is defined to be \$K(G) =< [g,alpha] gin G, alphain A >\$, which is a characteristic subgroup of G containing the derived sub- group \$G'\$ of \$G\$. A group is defined as A-perfect, if it equals its own autocommutator subgroup. The present research is aimed at classifying finite abelian groups which are A-perfect.
Keywords: Automorphism, Autocommutator subgroup, A, perfect group, Finite abelian group
• Alireza Khalili Asboei, Syyed Sadegh Salehi Amiri Page 15
Let G be a finite group and pi_{e}(G) be the set of element orders of G. Let k in pi_{e}(G) and m_{k} be the number of elements of order k in G. Let nse(G):={m_{k} | k in pi_{e}(G)}. In this paper, we prove that if G is a group such that nse(G)=nse(PSL(2, 25)), then G is isomorphic to PSL(2, 25).
Keywords: Element order, set of the numbers of elements of the same order, Sylow subgroup
• Changwen Li, Xiaolan Yi Page 21
In this paper, we investigate the influence of some subgrops of Sylow subgroups with semi cover-avoiding property and F-supplementation on the structure of finite groups and generalize a series of known results.
Keywords: semi cover, avoiding property, \$mathcal{F}\$, supplemented, \$p\$, nilpotent
• Hanieh Mirebrahimi, Behrooz Mashayekhy Page 33
Recently, the authors gave some conditions under which a direct product of finitely many groups is V-capable if and only if each of its factors is V-capable for some varieties V. In this paper, we extend this fact to any infi nite direct product of groups. Moreover, we conclude some results for V-capability of direct products of infi nitely many groups in varieties of abelian, nilpotent and polynilpotent group
Keywords: Capable group, Direct product, Variety of groups, V−capable group, direct limit
• Francesco De Giovanni, Caterina Rainone Page 39
A subgroup \$X\$ of a group \$G\$ is almost normal if the index \$|G:N_G(X)|\$ is finite, while \$X\$ is nearly normal if it has finite index in the normal closure \$X^G\$. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.
Keywords: Almost normality, nearly normality, normalizer subgroup
• Seyed Sadegh Salehi Amiri, Alireza Khalili Asboei, Ali Iranmanesh, Abolfazl Tehranian Page 51
Let G be a finite group and let Gamma(G) be the prime graphof G. Assume 2 < q = p^{alpha} < 100. We determine finite groupsG such that Gamma(G) = Gamma(U_3(q)) and prove that if q neq3, 5, 9, 17, then U_3(q) is quasirecognizable by prime graph,i.e., if G is a finite group with the same prime graph as thefinite simple group U_3(q), then G has a unique non-Abeliancomposition factor isomorphic to U_3(q). As a consequence of ourresults, we prove that the simple groups U_{3}(8) and U_{3}(11)are 4-recognizable and 2-recognizable by prime graph,respectively. In fact, the group U_{3}(8) is the first examplewhich is a 4-recognizable by prime graph.
Keywords: Prime graph, element order, simple group, linear group