Journal of the Iranian Mathematical Society
https://jims.ims.ir/
Journal of the Iranian Mathematical Societyendaily1Mon, 01 Jan 2024 00:00:00 +0330Mon, 01 Jan 2024 00:00:00 +0330A survey of recent results connected with subnormal subgroups
https://jims.ims.ir/article_179702.html
In this paper we give a brief survey of some highlights from the theory of subnormal subgroups and then reveal some recent extensions of this theory due to the current authors and others.On Infinite direct products of Rings modulo their direct sums
https://jims.ims.ir/article_180878.html
In this article, inspiring with a result due to O.A.S. Karamzadeh, we examine the $\prod_{i\in I} R_i/\oplus_{i\in I} R_i$, where $\{R_i\}_{i\in I}$ is an infinite family of rings. We observe that they are not self-injective on either side. In some important cases they are however $\aleph_0$-self-injective. Along this line, we study the interconnection between regularity(in the sense of von Neumann), injectivity and $\aleph_0$-injectivity.A note on arithmetic-geometric-harmonic mean inequality of several positive operators
https://jims.ims.ir/article_184321.html
&lrm;Suppose that $B_1,\cdots,B_m$ are positive operators on a Hilbert space $\mathcal{H}$&lrm;. &lrm;In this paper we generalize the weighted arithmetic&lrm;, &lrm;geometric and harmonic means as follows&lrm;:&lrm;\begin{align*}&lrm;&lrm;{\mathbf a_m}(\boldsymbol\kappa;\mathbf{B})&amp;={\mathbf a_2}(k_1,N';B_1,{\mathbf a_{m-1}}(\boldsymbol\kappa';\mathbf{B}'))=\frac{k_1B_1+\cdots+k_mB_m}{N}\\&lrm;&lrm;{\mathbf h_m}(\boldsymbol\kappa;\mathbf{B})&amp;={\mathbf h_2}(k_1,N';B_1,{\mathbf h_{m-1}}(\boldsymbol\kappa';\mathbf{B}'))=\left(\frac{k_1B_1^{-1}+\cdots+k_mB_m^{-1}}{N}\right)^{-1}\\&lrm;&lrm;{\mathbf g_m}(\boldsymbol\kappa;\mathbf{B})&amp;={\mathbf g_2}(k_1,N';B_1,{\mathbf g_{m-1}}(\boldsymbol\kappa';\mathbf{B}'))&lrm;&lrm;\end{align*}&lrm;&lrm;where $\boldsymbol\kappa=(k_1,\cdots,k_m)&lrm;, &lrm;N=k_1+\cdots+k_m&lrm;, &lrm;\boldsymbol\kappa'=(k_2,\cdots&lrm;, &lrm;k_m)$ and $N'=k_2+\cdots+k_m$&lrm;. &lrm;We show that the arithmetic-geometric-harmonic mean inequality holds&lrm;. &lrm;Also we investigate nine property of the geometric mean&lrm;.The unit group of the group algebra $\mathbb{F}_qD_{36}$
https://jims.ims.ir/article_187272.html
Abstract. Let p be a prime number and Fq be a finite field having q = pn elements and D36 be the dihedral group of order 36. The unit group U(FqD36), of the group algebra FqD36, has been completely characterized.Tsallis relative operator entropy properties with some weighted metrics
https://jims.ims.ir/article_190461.html
The present work attempts to provide some properties for Tsallis relative operator entropy $T_p(A | B)$, acting on positive definite matrices, with respect to weighted Hellinger and Alpha Procrustes distances. Many localizations of this operator have been determined. In particular, some estimations of the distances between $T_p(A | B)$ and some standard matrix means are outlined.Conciseness on normal subgroups and new concise words from outer commutator words
https://jims.ims.ir/article_191502.html
Let $w=w(x_1,\ldots,x_r)$ be an outer commutator word.
We show that the word $w(u_1,\ldots,u_r)$ is concise whenever $u_1,\ldots,u_r$ are non-commutator words in disjoint sets of variables.
This applies in particular to words of the form $w(x_1^{n_1},\ldots,x_r^{n_r})$, where the $n_i$ are non-zero integers.
Our approach is via the study of values of $w$ on normal subgroups, and in this setting we obtain the following result: if $N_1,\ldots,N_r$ are normal subgroups of a group $G$ and the set of all
values $w(g_1,\ldots,g_r)$ with $g_i\in N_i$ is finite then also the subgroup generated by these values, i.e.\ $w(N_1,\ldots,N_r)$, is finite.