منابع مشابه
Finite groups have even more centralizers
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
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Given a class C of subgroups of a topological group G, we say that a subgroup H ∈ C is a universal C subgroup of G if every subgroup K ∈ C is a continuous homomorphic pre-image of H. Such subgroups may be regarded as complete members of C with respect to a natural pre-order on the set of subgroups of G. We show that for any locally compact Polish group G, the countable power G has a universal K...
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Optical communications infrastructure is undergoing an intense development in his country now. A number of international investors and domestic operators are building from the beginning, modernizing or developing proprietary network or leasing wide area systems on a large scale. The aggregate level of these processes is of the order of bil. $. Despite of this the network is not homogeneous, has...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2016
ISSN: 0166-8641
DOI: 10.1016/j.topol.2015.12.065