فهرست مطالب

International Journal of Group Theory - Volume:2 Issue:4, 2013
  • Volume:2 Issue:4, 2013
  • تاریخ انتشار: 1392/03/09
  • تعداد عناوین: 7
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  • Rajendra Sharma, Pooja Yadav Pages 1-6
    Let Crn(Fp) denote the algebra of nXn circulant matrices over Fp, finite field of order p of prime characteristic p. The order of the unit groups U(Cr3(Fp)), U(Cr4(Fp)) and U(Cr5(Fp)) of algebras of circulant matrices over Fp are characterized.
    Keywords: Algebra, Unit Group, Circulant Matrices
  • Tao Zhao, Qingliang Zhang Pages 7-16
    Suppose that H is a subgroup of G, then H is said to be s-permutable in G, if H permutes with every Sylow subgroup of G. If HP=PH hold for every Sylow subgroup P of G with (|P|, |H|)=1), then H is called an s-semipermutable subgroup of G. In this paper, we say that H is partially S-embedded in G if G has a normal subgroup T such that HT is s-permutable in G and Hcap Tleq H_{overline{s}G}, where H_{overline{s}G} is generated by all s-semipermutable subgroups of G contained in H. We investigate the influence of some partially S-embedded minimal subgroups on the nilpotency and supersolubility of a finite group G. A series of known results in the literature are unified and generalized.
    Keywords: s, permutable subgroup, partially S, embedded subgroup, nilpotent group, formation
  • Alireza Abdollahi, S. Mohsen Ghoraishi Pages 17-20
    A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. Let G be a finite nonabelian p-group. It is known that if G is regular or of nilpotency class 2 or the commutator subgroup of G is cyclic, or G/Z(G) is powerful, then G has a noninner automorphism of order p leaving either the center Z(G) or the Frattini subgroup Phi(G) of G elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves Z(G) elementwise fixed.
    Keywords: Noninner automorphism, finite p, groups, the center
  • Viktoryia Kniahina, Victor Monakhov Pages 21-29
    In this paper we have found systems of subgroups in a finite group which $Bbb P$-subnormality guarantees supersolvability of the whole group.
    Keywords: Finite group, supersolvable group, $Bbb P$, subnormal subgroup
  • Ahmad Erfanian, Mohammad Farrokhi Derakhshandeh Ghouchan Pages 31-38
    Let $G$ be a finite group and $d_2(G)$ denotes the probability ‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $G$‎. ‎We ‎will obtain lower and upper bounds for $d_2(G)$ in the case where ‎the sets $E_G(x)={yin G:[y,x,x]=1}$ are subgroups of $G$ for ‎all $xin G$‎. ‎Also the given examples illustrate that all the ‎bounds are sharp.
    Keywords: Probabilityý, ý2, Engel conditioný, 3, metabelian
  • Sekhar Jyoti Baishya Pages 39-41
    A group G is said to be a C-tidy group if for every element x € G K(G), the set Cyc(x)={y € G | is cyclic} is a cyclic subgroup of G, where K(G) is the intersection of all the Cyc(x) in G. In this short note we determine the structure of finite C-tidy groups.
    Keywords: Finite groups, cyclicizers, C, tidy groups
  • The n-ary adding machine and solvable groups
    Josimar Da Silva Rocha, Said Sidki Pages 43-88
    We describe under a various conditions abelian subgroups of the automorphism group $Aut(T_n)$ of the regular $n$-ary tree $T_n$, which are normalized by the $n$-ary adding machine " $tau=(e,dots, e,tau)sigma_tau$" where $sigma_tau$" is the $n$-cycle $(0, 1,dots, n-1)$. As an application, for $n=p$ a prime number, and for $n=p^2$ when $p=2$, we prove that every finitely generated soluble subgroup of $Aut(T_n)$, containing $tau$ is an extension of a torsion-free metabelian group by a finite group.
    Keywords: Adding machine, Tree automorphisms, Automata, Solvable Groups