A set of quasi-uniform random variables X1, . . . , Xn may be generated from a finite group G and n of its subgroups, with the corresponding entropic vector depending on the subgroup structure of G. It is known that the set of entropic vectors obtained by considering arbitrary finite groups is much richer than the one provided just by abelian groups. In this paper, we start to investigate in mo...

We investigate the abelian category which is the target of intersection homology. Recall that, given a stratified space X, we get intersection homology groups IHnX depending on the choice of an n-perversity p. The n-perversities form a lattice, and we can think of IHnX as a functor from this lattice to abelian groups, or more generally R-modules. Such perverse R-modules form a closed symmetric ...

Suppose that n ≥ 2 and that S, T are sets of primes. Then the classification problem for the S-local torsion-free abelian groups of rank n is Borel reducible to the classification problem for the T -local torsion-free abelian groups of rank n if and only if S ⊆ T .

We study here some foundational aspects of the classification problem for torsionfree abelian groups of finite rank. These are, up to isomorphism, the subgroups of the additive groups (1n,­), for some n ̄ 1, 2, 3,... . The torsion-free abelian groups of rank% n are the subgroups of (1n,­). For n ̄ 1, that is, the subgroups of (1,­), the isomorphism problem was solved by Baer in the 1930s (see [10...

We define and investigate the class of almost ω1-n-simply presented p-torsion abelian groups, which class properly contains the subclasses of almost n-simply presented groups and ω1-n-simply presented groups, respectively. The obtained results generalize those obtained by us in Korean J. Math. (2014) and J. Algebra Appl. (2015).