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On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

Bartholdi, Laurent, Grigorchuk, Rostislav (2002)

Serdica Mathematical Journal

* The authors thank the “Swiss National Science Foundation” for its support.We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding quasi-regular representations are irreducible. These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representations. The Hecke algebras...

On residually finite groups and their generalizations

Andrzej Strojnowski (1999)

Colloquium Mathematicae

The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions asked in...

On semiabelian groups.

Kuzennyi, N.F., Subbotin, I.Ya. (2005)

International Journal of Mathematics and Mathematical Sciences

On soluble groups of automorphisms of nonorientable Klein surfaces

G. Gromadzki (1992)

Fundamenta Mathematicae

We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.

On soluble groups of module automorphisms of finite rank

Bertram A. F. Wehrfritz (2017)

Czechoslovak Mathematical Journal

Let R be a commutative ring, M an R -module and G a group of R -automorphisms of M , usually with some sort of rank restriction on G . We study the transfer of hypotheses between M / C M ( G ) and [ M , G ] such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose [ M , G ] is R -Noetherian. If G has finite rank, then M / C M ( G ) also is R -Noetherian. Further, if [ M , G ] is R -Noetherian and if only certain abelian sections...

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