Products of Protopological Groups
نویسنده
چکیده
Montgomery and Zippin saied that a group is approximated by Lie groups if every neighborhood of the identity contains an invariant subgroup H such that G/H is topologically isomorphic to a Lie group. Bagley, Wu, and Yang gave a similar definition, which they called a pro-Lie group. Covington extended this concept to a protopological group. Covington showed that protopological groups possess many of the characteristics of topological groups. In particular, Covington showed that in a special case, the product of protopological groups is a protopological group. In this note, we give a characterization theorem for protopological groups and use it to generalize her result about products to the category of all protopological groups. 2000 Mathematics Subject Classification. 22A99.
منابع مشابه
(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups
In this paper we determine the structure of (c,1,...,1) polynilpotent multiplier of certain class of groups. The method is based on the characterizing an explicit structure for the Baer invariant of a free nilpotent group with respect to the variety of polynilpotent groups of class row (c,1,...,1).
متن کاملBracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کاملIrreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$
We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$. We specialize the indeterminates used in defining these representations to non zero complex numbers. We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$. We then determine necessary and sufficient conditions that guarantee the irreducibility of th...
متن کاملAlkyl surface modification of nanoporous silica SBA-15 by click chemistry to obtain triazole products
In this study, Santa Barbara Amorphous (SBA-15) mesoporous silica has been functionalized with aminopropyl groups that were converted to propargyl-bearing moieties through the reaction with propargyl bromide. The material then underwent an efficient Cu(I)-catalyzed azide alkyne click reaction with sodium azide in order to obtain the corresponding triazole products. The covalent modification of ...
متن کاملEffects of dairy Products on Fasting Blood Glucose, Insulin Resistance, Blood Pressure, and Lipid Profile in Patients with Type 2 Diabetes: A Randomized, Controlled Clinical Trial
Introduction: This randomized controlled clinical trial aimed to investigate the effects of dairy product consumption on fasting blood glucose, insulin resistance, blood pressure, and lipid profile in patients with type 2 diabetes. Materials and Methods: Ninety-one diabetic patients were randomly assigned to one of the following three groups: group A, <1 serving of dairy products per day; group...
متن کامل