The Sylow p-Subgroups of a Limiting (Stable) Linear Group over an Algebraically Closed Field

In Math. Zh. 36(3) (1963), 240–246, we considered the classification of Sylow p-subgroups of a countable (finitary) symmetric group. Later, we extended this classification to Sylow p-subgroups of a limiting (stable) linear group over a finite field GF(q) with char(GF(q)) p. In this paper, the classification of the Sylow p-subgroups of the limiting (stable) linear group GL() is given for an algebraically closed field of characteristic p. Every Sylow p-subgroup is characterized by a p-adic integer together with a finite or countable cardinal.     

Subgroup transitivity in abelian groups

We generalize an appropriate modification of the classical notion of transitivity in abelian -groups from one that is based on elements to one based on subgroups. We consider those -groups that are transitive in the sense that there is an automorphism of the group that maps one isotype subgroup onto any other isotype subgroup , unless this is impossible due to the simple reason that either the subgroups are not isomorphic or the quotient groups are not (as valuated groups when endowed with the coset valuation). Slight variations of this are used to define the classes of strongly transitive and strongly U-transitive groups. The latter class is studied in some detail in this paper, and it is shown that every -group is strongly transitive with respect to countable isotype subgroups.

     

Minimal Geodesics and Nilpotent Fundamental Groups

Hedlund [18] constructed Riemannian metrics on n-tori, n 3 for which minimal geodesics are very rare. In this paper we construct similar examples for every nilpotent fundamental group. These examples show that Bangert's existence results of minimal geodesics [4] are optimal for nilpotent fundamental groups.     

Exponent preserving subgroups of the finite simple groups

Given a group G denote with exp(G) its exponent, which is the least common multiple of the order of its elements. In this paper, we solve the problem of finding the finite simple groups having a proper subgroup with the same exponent. For each G with this property we will provide an explicit example of H<G with exp(G)?=?exp(H).     

环上线性群的子群结构

本文主要讨论欧氏整环上线性群一类子群的结构,并获得其一类极大子群,     

Synthetic receptors for selectively detecting erythrocyte ABO subgroups

Surface imprinting techniques with erythrocytes as templates yield polymer coatings with selective recognition sites towards red blood cells. The resulting cavities in the respective surface exhibit selectivity between blood subgroups as shown by Quartz Crystal Microbalance (QCM) measurements. Mass sensitive effects in the kilohertz range could be observed for concentrations down to 0.5 × 10⁸ cells/mL. Frequency response as well as recovery of the sensor took place within a few minutes, indicating that no covalent binding is involved. Linear concentration dependence over a defined region provides ideal conditions for cross selectivity measurements. A₁ imprinted sensor coatings resulted in an effect of 40 kHz when exposed to the template blood group, while A₂ erythrocytes yielded just 11% of that value on the same layer. Furthermore, A₂ imprinted coatings incorporated only one third the amount of A₁ erythrocytes as compared to A₂ ones. Therefore, imprinted materials depict the entire cell surface and utilize it for recognition, whereas natural antibodies bind on the defined antigen position and thus usually cannot distinguish between cells carrying different amounts of them.     

On sse-embedded subgroups of finite groups

Abstract

In this paper, we introduce the concept of sse-embedded subgroups of finite groups and present some new characterizations of solubility of finite groups using the sse-embedding property of subgroups. Furthermore, we discuss the sse-embedded subgroups in finite nonabelian simple groups. Some previously known results are generalized and unified.     

On g-s-supplemented subgroups of finite groups

A subgroup H of a group G is said to be g-s-supplemented in G if there exists a subgroup K of G such that HK⊴G and H ∩ K ⩽ H _sG , where H_sG is the largest s-permutable subgroup of G contained in H. By using this new concept, we establish some new criteria for a group G to be soluble.