فهرست مطالب

  • Volume:3 Issue:4, 2014
  • تاریخ انتشار: 1393/01/28
  • تعداد عناوین: 9
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  • Robert Heffernan, Des Machale, Aine Ni She Pages 1-12
    We consider two commutativity ratios $Pr(G)$ and $f(G)$ in a finite group $G$ and examine the properties of $G$ when these ratios are `large''. We show that if $Pr(G) > frac{7}{24}$, then $G$ is metabelian and we give threshold results in the cases where $G$ is insoluble and $G''$ is nilpotent. We also show that if $f(G) > frac{1}{2}$, then $f(G) = frac{n+1}{2n}$, for some natural number $n$.
    Keywords: commutativity ratios, commuting probability, Finite groups
  • Neha Makhijani, R. K. Sharma, J. B. Srivastava Pages 13-16
    Let $Cr_{n}(F)$ denote the algebra of $n times n$ circulant matrices over the field $F$. In this paper, we study the unit group of $Cr_{n}(F_{p^m})$, where $F_{p^m}$ denotes the Galois field of order $p^{m}$, $p$ prime.
    Keywords: Group Algebra, Unit Group, Circulant Matrices
  • Tao Zhao Pages 17-25
    A subgroup H is said to be s-permutable in a group G, if HP=PH hold for every Sylow subgroup P of G. If there exists a subgroup B of G such that HB=G and H permutes with every Sylow subgroup of B, then H is said to be SS-quasinormal in G. In this paper, we say that H is a weakly SS-quasinormal subgroup of G, if there is a normal subgroup T of G such that HT is s-permutable and Hcap T is SS-quasinormal in G. By assuming that some subgroups of G with prime power order have the weakly SS-quasinormal properties, we get some new characterizations about the hypercyclically embedded subgroups of G. A series of known results in the literature are unified and generalized.
    Keywords: s, permutable, weakly SS, quasinormal, p, nilpotent, hypercyclically embedded
  • Jinshan Zhang, Guangju Zeng, Zhencai Shen Pages 27-31
    The aim of this note is to characterize the finitegroups in which all non-linear irreducible characters have distinct zero entries number.
    Keywords: Finite groups, characters, zeros of characters
  • Jiangtao Shi Pages 33-36
    Let $G=SL_2(p^f)$ be a special linear group and $P$ be a Sylow $2$-subgroup of $G$, where $p$ is a prime and $f$ is a positive integer such that $p^f>3$. By $N_G(P)$ we denote the normalizer of $P$ in $G$. In this paper, we show that $N_G(P)$ is nilpotent (or $2$-nilpotent, or supersolvable) if and only if $p^{2f}equiv 1,(mod 16)$.
    Keywords: special linear group, Sylow subgroup, normalizer, nilpotent, supersolvable
  • Olga Dashkova Pages 37-46
    The author studies the $bf R$$G$-module $A$ such that $bf R$ is an associative ring, a group $G$ has infinite section $p$-rank (or infinite 0-rank), $C_{G}(A)=1$, and for every proper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $A/C_{A}(H)$ is a finite $bf R$-module. It is proved that if the group $G$ under consideration is locally soluble then $G$ is a soluble group and $A/C_{A}(G)$ is a finite $bf R$-module.
    Keywords: group ring, linear group, module
  • Behrooz Khosravi, Hossein Moradi Pages 47-56
    ‎Let G be a finite group‎. ‎In [Ghasemabadi et al.‎, ‎characterizations of the simple group 2 D n (3) by prime graph‎ ‎and spectrum‎, ‎Monatsh Math.‎, ‎2011] it is‎ ‎proved that if n is odd‎, ‎then 2 D n (3) is recognizable by‎ ‎prime graph and also by element orders‎. ‎In this paper we prove‎ ‎that if n is even‎, ‎then D= 2 D n (3) is quasirecognizable by‎ ‎prime graph‎, ‎i.e‎. ‎every finite group G with Γ(G)=Γ(D) ‎ ‎has a unique nonabelian composition factor and this factor is isomorphic to‎ ‎D ‎.
    Keywords: Prime graph, simple group, linear group, quasirecognition
  • Francesco De Giovanni, Martin L. Newell, Alessio Russo Pages 57-61
    ‎Motivated by a celebrated theorem of Schur‎, ‎we show that if~Γ is a normal subgroup of the full automorphism group Aut(G) of a group G such that Inn(G) is contained in Γ and Aut(G)/Γ has no uncountable abelian subgroups of prime exponent‎, ‎then [G,Γ] is finite‎, ‎provided that the subgroup consisting of all elements of G fixed by Γ has finite index‎. ‎Some applications of this result are also given.‎
    Keywords: Automorphism group, Schur's theorem, absolute centre
  • Esmaeil Babaei, Yousef Zamani Pages 63-69
    ‎Let G i be a subgroup of S m i ‎,‎ 1≤i≤k ‎. ‎Suppose χ i is an irreducible complex character of G i ‎. ‎We consider G 1 ×⋯×G k as subgroup of S m ‎, ‎where m=m 1 +⋯‎+‎m k ‎. ‎In this paper‎, ‎we give a formula for the dimension of H d (G 1 ×⋯×G k ‎,‎χ 1 ×⋯×χ k) and investigate the existence of an o-basis of this type of classes‎.
    Keywords: Symmetric polynomials, symmetry class of polynomialsý, ýorthogonal basis, ýpermutaion groupsý, ýcomplex characters