Let K be an algebraic number field with ring of integers OK , p > 2, be a rational prime and G the cyclic group of order p. Let Λ denote the order OK [G]. Let Cl(Λ) denote the locally free class group of Λ and D(Λ) the kernel group, the subgroup of Cl(Λ) consisting of classes that become trivial upon extension of scalars to the maximal order. If p is unramified in K, then D(Λ) = T (Λ), where T ...

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

w Statement of the theorem 1.1. Let G be a reductive p-adic group. A smooth representation (~', E) of the group G on a complex vector space E is called a G-module. Usually we shorten the notation and write w or E. Let d~(G) be the category of G-modules, Irr G the set of equivalence classes of irreducible G-modules, and R (G) the Grothendieck group of G-modules of fnite length; R(G) is a free ab...

Let G be the group scheme SL d + 1 over Z and let Q parabolic subgroup corresponding to simple roots ? 2 , ? ? . Then / is -scheme of partial flags { D ? H V } We will calculate cohomology modules line bundles this flag scheme. prove that only non-trivial ones are isomorphic kernel or cokernel certain matrices with multinomial coefficients.

OBJECTIVES To evaluate the association between fracture risk and levothyroxine use in elderly women with hypothyroidism, according to previous osteoporosis history. METHODS We conducted a cohort study from the Korean Health Insurance Review and Assessment Service claims database from January 2005 to June 2006. The study population comprised women aged ≥65 years who had been diagnosed with hyp...

In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.

 ‎Let $tilde{F}=(Q,S,tilde{R},Z,omega,tilde{delta},‎ F_1,F_2)$‎ ‎be a general fuzzy automaton and the set of its states be a group.‎ ‎The aim of this paper is the study of applications of a group in a‎ ‎general fuzzy automaton‎. ‎For this purpose‎, ‎we define the concepts‎ ‎of fuzzy normal kernel of a general fuzzy automaton‎, ‎fuzzy kernel‎ ‎of a general fuzzy automaton‎, ‎adjustable‎, ‎multip...

We demonstrate that two supersoluble complements of an abelian base in a finite split extension are conjugate if and only if, for each prime $p$, Sylow $p$-subgroup one complement is to the other. As corollary, we find any subgroup $N$ $G$ there exists $S$ such $S\cap N$ $G$. In particular, restricting groups allows us ease D. G. Higman's stipulation be within $S$. then consider group actions o...

In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order p 22 tends to infinity with p. More precisely, for each prime number p there is a family (M λ) λ=0,... ,p−1 of indecom-posable and pairwise nonisomorphic metabelian p-groups of the given order. In this manuscript we use recent results on the classification of possible embeddings of a ...

In this paper, we resolve a conjecture of Green and Liebeck (2019) [3] on codes in PGL(2,q). To be specific, show that: if D is dihedral subgroup order 2(q+1) G=PGL(2,q), A={g∈G:gq+1=1,g2≠1}, then λG=A⋅D, where λ=q or q−1 according as q even odd.