Between 1952 and 1954 Amitsur and Kurosh initiated the general theory of radicals in various contexts. In the case of all groups some interesting results concerning radicals were obtained by Kurosh, Shchukin, Ryabukhin, Gardner and others. In this paper we are going to examine radical theory in the class of all finite groups. This strong restriction gives chance to obtain stronger results, then...

In this paper, we obtain an explicit formula for the number of zero-sum k-element subsets in any finite abelian group.

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

We consider $2$-colourings $f : E(G) \rightarrow \{ -1 ,1 \}$ of the edges a graph $G$ with colours $-1$ and $1$ in $\mathbb{Z}$. A subgraph $H$ is said to be zero-sum under $f$ if $f(H) := \sum_{e\in E(H)} f(e) =0$. study following type questions, several cases obtaining best possible results: Under which conditions on $|f(G)|$ can we guarantee existence spanning tree $G$? The types are comple...

In this paper, we obtain the general solution and the generalized   Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1, i...

We calculate the on-shell Σ-Λ mixing parameter θ with the method of QCD sum rule. Our result is θ(m Σ ) = (−)(0.5 ± 0.1) MeV. The electromagnetic interaction is not included.

We define an atom tree of a graph as a generalization of a clique tree: its nodes are the atoms obtained by clique minimal separator decomposition, and its edges correspond to the clique minimal separators of the