A useful category for mixed Abelian groups.
A variation of Thompson's conjecture for the symmetric groups
Let be a finite group and let denote the set of conjugacy class sizes of . Thompson’s conjecture states that if is a centerless group and is a non-abelian simple group satisfying , then . In this paper, we investigate a variation of this conjecture for some symmetric groups under a weaker assumption. In particular, it is shown that if and only if and has a special conjugacy class of size , where is a prime number. Consequently, if is a centerless group with , then .
A version of Brauer’s theorem for integer central functions
In this article we prove an effective version of the classical Brauer’s Theorem for integer class functions on finite groups.
A very short proof of Forester's rigidity result.
A Very Simple Proof of Bott's Theorem.
A volume form on the SU(2)-representation space of knot groups.
A weak type (1,1) estimate for a maximal operator on a group of isometries of a homogeneous tree
We give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy-Littlewood and spherical maximal operators, are of weak type (1,1). This result extends to corresponding maximal operators on a transitive group of isometries of the tree, and in particular for (nonabelian finitely generated) free groups.
A -theorem for -injectors in finite groups
A -ring Frobenius characteristic for .
Abelian Extensions of Arbitrary Fields.
Abelian Factorizations of Infinite Groups.
Abelian group extensions and the axiom of constructibility.
Abelian group pairs having a trivial coGalois group
Torsion-free covers are considered for objects in the category Objects in the category are just maps in -Mod. For we find necessary and sufficient conditions for the coGalois group associated to a torsion-free cover, to be trivial for an object in Our results generalize those of E. Enochs and J. Rado for abelian groups.
Abelian groups have/are near Frattini subgroups
The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.
Abelian groups in a topos of sheaves: Torsion and essential extensions.
Abelian groups in which every pure subgroup is an isotype subgroup
Abelian groups in which every -isotype subgroup is a pure subgroup, resp. an isotype subgroup
Abelian groups of zero adjoint entropy
The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint...
Abelian groups that cannot be factored without periodic factor
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.