More Abelian Groups with Free Duals
نویسنده
چکیده
In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup G of the additive group Zω is constructed whose dual, Hom(G,Z), is free abelian of rank 2א0 . The question of whether Zω has subgroups whose duals are free of still higher rank is discussed, and some further classes of subgroups of Zω are noted.
منابع مشابه
אn-Free Modules With Trivial Duals
In the first part of this paper we introduce a simplified version of a new Black Box from Shelah [11] which can be used to construct complicated אn-free abelian groups for any natural number n ∈ N. In the second part we apply this prediction principle to derive for many commutative rings R the existence of אn-free R-modules M with trivial dual M ∗ = 0, where M∗ = Hom(M, R). The minimal size of ...
متن کاملON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS
Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.
متن کاملOn Unitary Representability of Topological Groups
We prove that the additive group (E∗, τk(E)) of an L∞-Banach space E, with the topology τk(E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving that the topological group (E∗, τk(E)) is uniformly homeomorphic to a subset of ` κ 2 for some κ. As an immediat...
متن کاملNon-Abelian Duality and Canonical Transformations
We construct explicit canonical transformations producing non-abelian duals in principal chiral models with arbitrary group G. Some comments concerning the extension to more general σ-models, like WZW models, are given. PUPT-1532 hep-th/9503045 March 1995 ∗[email protected]
متن کاملThe Duals of Warfield
A Warreld group is a direct summand of a simply presented abelian group. In this paper, we describe the Pon-trjagin dual groups of Warreld groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.
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 2012