منابع مشابه
On Whitehead Precovers
It is proved undecidable in ZFC + GCH whether every Z-module has a {Z}-precover. Let F be a class of R-modules of the form C = {A : Ext(A,C) = 0 for all C ∈ C} for some class C. The first author and Jan Trlifaj proved [7] that a sufficient condition for every module M to have an F -precover is that there is a module B such that F = {B} (= {A : Ext(B,A) = 0}). In [8], generalizing a method used ...
متن کاملOn a conjecture of Street and Whitehead on locally maximal product-free sets
Let S be a non-empty subset of a group G. We say S is product-free if S ∩ SS = ∅, and S is locally maximal if whenever T is product-free and S ⊆ T , then S = T . Finally S fills G if G∗ ⊆ S t SS (where G∗ is the set of all non-identity elements of G), and G is a filled group if every locally maximal product-free set in G fills G. Street and Whitehead [8] investigated filled groups and gave a cl...
متن کاملOn Generalized Whitehead Products
We define a symmetric monodical pairing G ◦ H among simply connected co-H spaces G and H with the property that S(G◦H) is equivalent to the smash product G∧H as co-H spaces. We further generalize the Whitehead product map to a map G ◦ H → G ∨ H whose mapping cone is the cartesian product. Whitehead products have played an important role in unstable homotopy. They were originally introduced [Whi...
متن کاملOn the genericity of Whitehead minimality
We show that a finitely generated subgroup of a free group, chosen uniformly at random, is strictly Whitehead minimal with overwhelming probability. Whitehead minimality is one of the key elements of the solution of the orbit problem in free groups. The proofs strongly rely on combinatorial tools, notably those of analytic combinatorics. The result we prove actually depends implicitly on the ch...
متن کاملThe Euler Characteristic of the Whitehead Automorphism Group of a Free Product
A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups. In particular, we establish formulae for the Euler characteristics of: the group of Whitehead automorphisms Wh(∗ i=1 Gi) when the Gi are of finite homological type; Aut(∗ i=1...
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ژورنال
عنوان ژورنال: Journal of Homotopy and Related Structures
سال: 2016
ISSN: 2193-8407,1512-2891
DOI: 10.1007/s40062-016-0153-z