Cartesian products as profinite completions

نویسندگان

  • Martin Kassabov
  • Nikolay Nikolov
چکیده

We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups under some natural restrictions.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Profinite completions of some groups acting on trees

We investigate the profinite completions of a certain family of groups acting on trees. It turns out that for some of the groups considered, the completions coincide with the closures of the groups in the full group of tree automorphisms. However, we introduce an infinite series of groups for which that is not so, and describe the kernels of natural homomorphisms of the profinite completions on...

متن کامل

Profinite Heyting Algebras and Profinite Completions of Heyting Algebras

This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...

متن کامل

Comparison of MacNeille, Canonical, and Profinite Completions

Using duality theory, we give necessary and sufficient conditions for the MacNeille, canonical, and profinite completions of distributive lattices, Heyting algebras, and Boolean algebras to be isomorphic.

متن کامل

Profinite groups, profinite completions and a conjecture of Moore

Let R be any ring (with 1), Γ a group and RΓ the corresponding group ring. Let H be a subgroup of Γ of finite index. Let M be an RΓ−module, whose restriction to RH is projective. Moore’s conjecture [5]: Assume for every nontrivial element x in Γ, at least one of the following two conditions holds: M1) 〈x〉 ∩ H 6= {e} (in particular this holds if Γ is torsion free) M2) ord(x) is finite and invert...

متن کامل

On profinite completions and canonical extensions

We show that if a variety V of monotone lattice expansions is finitely generated, then profinite completions agree with canonical extensions on V . The converse holds for varieties of finite type. It is a matter of folklore that the profinite completion of a Boolean algebra B is given by the power set of the Stone space of B, or in the terminology of Jónsson and Tarski [5], by the canonical ext...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008