نتایج جستجو برای: abelian group
تعداد نتایج: 993306 فیلتر نتایج به سال:
given an integer $n$, we denote by $mathfrak b_n$ and $mathfrak c_n$ the classes of all groups $g$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $g$, respectively. in this paper we give a characterization for groups in $mathfrak b_n$ and for groups in $mathfrak c_n$. we also obtain an arithmetic description of the set of all integers $n$ such that a gr...
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 autocommutator of $gin g$ and $alphain a$. also, the autocommutator subgroup of g is defined to be $k(g)=langle[g,alpha]|gin g, alphain arangle$, which is a characteristic subgroup of $g$ containing the derived subgroup $g'$ of $g$. a group is defined...
we commence by using from a new norm on l1(g) the -algebra of all integrable functions on locally compact group g, to make the c-algebra c(g). consequently, we find its dual b(g), which is a banach algebra so-called fourier-stieltjes algebra, in the set of all continuous functions on g. we consider most of important basic theorems about this algebra. this consideration leads to a rather com...
Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...
a group is called morphic if for each normal endomorphism α in end(g),there exists β such that ker(α)= gβ and gα= ker(β). in this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= gβ and gα = ker(γ). we call g quasi-morphic, if this happens for any normal endomorphism α in end(g). we get the following results: g is quasi-morphic if and only if, for any ...
let $pounds$ be the category of all locally compact abelian (lca) groups. in this paper, the groups $g$ in $pounds$ are determined such that every extension $0to xto yto gto 0$ with divisible, $sigma-$compact $x$ in $pounds$ splits. we also determine the discrete or compactly generated lca groups $h$ such that every pure extension $0to hto yto xto 0$ splits for each divisible group $x$ ...
a $p$-group $g$ is $p$-central if $g^{p}le z(g)$, and $g$ is $p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin g$. we prove that for $g$ a finite $p^{2}$-abelian $p$-central $p$-group, excluding certain cases, the order of $g$ divides the order of $text{aut}(g)$.
let $g$ be a group and $aut(g)$ be the group of automorphisms of$g$. for any naturalnumber $m$, the $m^{th}$-autocommutator subgroup of $g$ is definedas: $$k_{m}(g)=langle[g,alpha_{1},ldots,alpha_{m}] |gin g,alpha_{1},ldots,alpha_{m}in aut(g)rangle.$$in this paper, we obtain the $m^{th}$-autocommutator subgroup ofall finite abelian groups.
a $p$-group $g$ is $p$-central if $g^{p}le z(g)$, and $g$ is $p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin g$. we prove that for $g$ a finite $p^{2}$-abelian $p$-central $p$-group, excluding certain cases, the order of $g$ divides the order of $text{aut}(g)$.
let $gamma$ be a normal subgroup of the full automorphism group $aut(g)$ of a group $g$, and assume that $inn(g)leq gamma$. an endomorphism $sigma$ of $g$ is said to be {it $gamma$-central} if $sigma$ induces the the identity on the factor group $g/c_g(gamma)$. clearly, if $gamma=inn(g)$, then a $gamma$-central endomorphism is a {it central} endomorphism. in this article the conditi...
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