Abstract Crystal structures connected by continuous phase transitions are linked through mathematical relations between crystallographic groups and their subgroups. In the present study, we introduce group-subgroup machine learning (GS-ML) show that including materials with small unit cells in training set decreases out-of-sample prediction errors for large cells. GS-ML incurs least cost to rea...

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.

Red hot pepper is a plant that belongs to the Solanaceae family and is known as Capsicum annuum. Capsaicin is the active ingredient of cayenne pepper. Ghrelin is a hormone, which consists of polypeptide structure. Ghrelin also contributes to growth hormone secretion, energy balance, food intake and body weight regulator. The aim of this study was the localization and expression of ghrelin in th...

this is a survey article on centralizers of finite‎ ‎subgroups in locally finite‎, ‎simple groups or lfs-groups as we‎ ‎will call them‎. ‎we mention some of the open problems about‎ ‎centralizers of subgroups in lfs-groups and applications of the‎ ‎known information about the centralizers of subgroups to the‎ ‎structure of the locally finite group‎. ‎we also prove the‎ ‎following‎: ‎let $g$ be...

The present article is a summary of joint work of the author and Phillip Wesolek on the normal subgroup structure of totally disconnected locally compact second-countable (t.d.l.c.s.c.) groups. The general strategy is as follows: We obtain normal series for a t.d.l.c.s.c. group in which each factor is ‘small’ or a non-abelian chief factor; we show that up to a certain equivalence relation (call...