On the Divisible Parts of Quotient Groups
نویسندگان
چکیده
We study the possible cardinalities of the divisible part of G/K when the cardinality of K is known and when, for all countable subgroups C of G, the divisible part of G/C is countable.
منابع مشابه
Divisible Groups Derived from Divisible Hypergroups
The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...
متن کاملModules over the Ring of Pseudorational Numbers and Quotient Divisible Groups
Structure theorems are obtained for some classes of modules over the ring of pseudorational numbers and some classes of quotient divisible mixed groups.
متن کاملnon-divisibility for abelian groups
Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
متن کاملThe Module of Pseudo-rational Relations of a Quotient Divisible Group
It is proved that the module of pseudo-rational relations determines a quotient divisible group up to quasi-isomorphism.
متن کاملSemi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1993