Title:

On lattices of closed subgroups in the group of infinite triangular matrices over a field

Creator:

Bier, Agnieszka

Abstract:

We investigate a special type of closed subgroups of the topological group UT(∞, K) of infinite-dimensional unitriangular matrices over a field K (|K| > 2), considered with the natural inverse limit topology. Namely, we generalize the concept of partition subgroups introduced in [23] and define partition subgroups in UT(∞,K). We show that they are all closed and discuss the problem of their invariancy to various group homomorphisms. We prove that a characteristic subgroup of UT(∞,K) is necessarily a partition subgroup and characterize the lattices of characteristic and fully characteristic subgroups in UT(∞, K). We conclude with some implications of the given characterization on verbal structure of UT(∞, K) and T(∞, K) and use some topological properties to discuss the problem of the width of verbal subgroups in groups defined over a finite field K.

Keywords:

nieskończona macierz trójkątna ; podgrupa werbalna ; podgrupa charakterystyczna ; podgrupa zamknięta

Date:

2015

Format:

application/pdf

Resource Identifier:

Baza Wiedzy PŚ

Source:

Linear Algebra and Its Applications 2015 vol. 485, s. 132-152

Language:

eng

Relation:

Wydział Matematyki Stosowanej. Politechnika Śląska

Access:

zasób dostępny bez ograniczeń

Licence:

CC BY 3.0