Groups which are an infinite cyclic extension of a unique base group
نویسندگان
چکیده
منابع مشابه
Which elements of a finite group are non-vanishing?
Let $G$ be a finite group. An element $gin G$ is called non-vanishing, if for every irreducible complex character $chi$ of $G$, $chi(g)neq 0$. The bi-Cayley graph ${rm BCay}(G,T)$ of $G$ with respect to a subset $Tsubseteq G$, is an undirected graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin G, tin T}$. Let ${rm nv}(G)$ be the set of all non-vanishi...
متن کاملFinite groups all of whose proper centralizers are cyclic
A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic. In this article we determine all finite $CC$-groups.
متن کامل2 00 8 Which infinite abelian torsion groups admit an almost maximally almost - periodic group topology ? *
A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that (a) every countably infinite abelian torsion group, (b) every abelian torsion group of cardinality greater than continuum, and (c) every (non-trivial) divisible abelian torsion group admits a (Hausdorff) almost maximally almost-periodic gr...
متن کاملWhich Infinite Abelian Groups Admit an Almost Maximally Almost-periodic Group Topology?
A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that every abelian group with an infinite torsion subgroup admits a (Hausdorff) almost maximally almost-periodic group topology. Some open problems are also formulated.
متن کاملwhich elements of a finite group are non-vanishing?
let $g$ be a finite group. an element $gin g$ is called non-vanishing, if for every irreducible complex character $chi$ of $g$, $chi(g)neq 0$. the bi-cayley graph $bcay(g,t)$ of $g$ with respect to a subset $tsubseteq g$, is an undirected graph with vertex set $gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin g, tin t}$. let $nv(g)$ be the set of all non-vanishing element...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1977
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700019649