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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 permutability in semigroup varieties

Bedřich Pondělíček (1991)

Mathematica Bohemica

The paper contains characterizations of semigroup varieties whose semigroups with one generator (two generators) are permutable. Here all varieties of regular * -semigroups are described in which each semigroup with two generators is permutable.

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