On generations by conjugate elements in almost simple groups with socle \mbox{}^2F_4(q^2)'

We prove that if L=\mbox{}^2F_4(2^{2n+1})' and $x$ is a nonidentity automorphism of $L$ then $G=\langle L,x\rangle$ has four elements conjugate to $x$ that generate $G$. This result is used to study the following conjecture about the $\pi$-radical of a finite group: Let $\pi$ be a proper subset of the set of all primes and let $r$ be the least prime not belonging to $\pi$. Set $m=r$ if $r=2$ or $3$ and set $m=r-1$ if $r\geqslant 5$. Supposedly, an element $x$ of a finite group $G$ is contained in the $\pi$-radical $\operatorname{O}_\pi(G)$ if and only if every $m$ conjugates of $x$ generate a $\pi$-subgroup. Based on the results of this paper and a few previous ones, the conjecture is confirmed for all finite groups whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, or unitary simple group, or to one of the groups of type ${}^2B_2(2^{2n+1})$, ${}^2G_2(3^{2n+1})$, ${}^2F_4(2^{2n+1})'$, $G_2(q)$, or ${}^3D_4(q)$

Finite groups whose maximal subgroups have the hall property

We study the structure of finite groups whosemaximal subgroups have the Hall property. We prove that such a group G has at most one non-Abelian composition factor, the solvable radical S(G) admits a Sylow series, the action of G on sections of this series is irreducible, the series is invariant with respect to this action, and the quotient group G/S(G) is either trivial or isomorphic to PSL2(7), PSL2(11), or PSL5(2). As a corollary, we show that every maximal subgroup of G is complemented. © 2013 Allerton Press, Inc

On embedding theorems for X\mathfrak{X}-subgroups

Let $\mathfrak{X}$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1963-64: For a given $\mathfrak{X}$-subgroup $K$ and maximal $\mathfrak{X}$-subgroup $H$, is it possible to see embeddability of $K$ in $H$ (up to conjugacy) by their projections onto the factors of a fixed subnormal series. On the one hand, we construct examples where $K$ has the same projections as some subgroup of $H$ but is not conjugate to any subgroup of $H$. On the other hand, we prove that if $K$ normalizes the projections of a subgroup $H$, then $K$ is conjugate to a subgroup of $H$ even in the more general case when $H$ is a submaximal $\mathfrak{X}$-subgroup

Bacterial Cellulose/Alginate Nanocomposite for Antimicrobial Wound Dressing

Development of novel wound dressing has attracted more and more attentions in recent years. Bacterial cellulose is a biopolymer of great potentials, which features a distinctive three-dimensional structure consisting of an ultrafine network of cellulos nanofibers. In the present study, nanocomposite bacterial cellulose films modified in situ by the addition of alginate during the static cultivation of Gluconacetobacter sucrofermentans B-11267 were produced and then enriching the polymer with an antimicrobial agent tetracycline hydrochloride. The structure of bacterial cellulose and nanocomposite was analyzed by AFM and FTIR. The FTIR spectra displayed the specified interaction between the hydroxyl group of cellulose and the carboxyl group of alginate. The produced bacterial cellulose and nanocomposite were analyzed to determine tensile modulus. The antibacterial activity of nanocomposites were investigated by disk diffusion method. The resulting nanocomposite have high antibiotic activity against Staphylococcus aureus and can be used in medicine as a wound dressing. Keywords: bacterial cellulose, Gluconacetobacter sucrofermentans, alginate, nanocomposite, antibacterial activity, wound dressin

Role of membrane lipids in the regulation of erythrocytic oxygen-transport function in cardiovascular diseases

The composition and condition of membrane lipids, the morphology of erythrocytes, and hemoglobin distribution were explored with the help of laser interference microscopy (LIM) and Raman spectroscopy. It is shown that patients with cardiovascular diseases (CVD) have significant changes in the composition of their phospholipids and the fatty acids of membrane lipids. Furthermore, the microviscosity of the membranes and morphology of the erythrocytes are altered causing disordered oxygen transport by hemoglobin. Basic therapy carried out with the use of antiaggregants, statins, antianginals, beta-blockers, and calcium antagonists does not help to recover themorphofunctional properties of erythrocytes. Based on the results the authors assume that, for the relief of the ischemic crisis and further therapeutic treatment, it is necessary to include, in addition to cardiovascular disease medicines, medication that increases the ability of erythrocytes’ hemoglobin to transport oxygen to the tissues. We assume that the use of LIM and Raman spectroscopy is advisable for early diagnosis of changes in the structure and functional state of erythrocytes when cardiovascular diseases develop

On the pronormality of subgroups of odd index in some direct products of finite groups

subgroup H of a group G is said to be pronormal in G if H and Hg are conjugate in (H,Hg) for each g ∈ G. Some problems in Finite Group Theory, Combinatorics and Permutation Group Theory were solved in terms of pronormality, therefore, the question of pronormality of a given subgroup in a given group is of interest. Subgroups of odd index in finite groups satisfy a native necessary condition of pronormality. In this paper, we continue investigations on pronormality of subgroups of odd index and consider the pronormality question for subgroups of odd index in some direct products of finite groups. In particular, in this paper, we prove that the subgroups of odd index are pronormal in the direct product G of finite simple symplectic groups over fields of odd characteristics if and only if the subgroups of odd index are pronormal in each direct factor of G. Moreover, deciding the pronormality of a given subgroup of odd index in the direct product of simple symplectic groups over fields of odd characteristics is reducible to deciding the pronormality of some subgroup H of odd index in a subgroup of Qt i=1 Z3 Symni , where each Symni acts naturally on {1, . . . ,ni}, such that H projects onto Qt i=1 Symni . Thus, in this paper, we obtain a criterion of pronormality of a subgroup H of odd index in a subgroup of Qt i=1 Zpi Symni , where each pi is a prime and each Symni acts naturally on {1, . . . , ni}, such that H projects onto Qt i=1 Symni . © 2023 World Scientific Publishing Company