We provide an example of a non-finitely generated group which admits nonempty strongly aperiodic subshift finite type. Furthermore, we completely characterize the groups with this property in terms their finitely subgroups and roots conjugacy classes.

Let [Formula: see text] be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if normal subgroup group then the image an text]-maximal in not, general, text]. We say reduction text]-theorem holds for if, every extension (i.e. contains as subgroup), number conjugacy classes subgroups same. The implies In this paper, we prove only all are c...

Abstract In this paper, we set ? ? ( G stretchy="false">) \eta(G) to be the number of conjugacy classes maximal cyclic subgroups a finite group ????. We compute for all metacyclic ????-groups. show that if ???? is ????-group order <m:msup...

We construct an explicit quantization of semi-simple conjugacy classes of the complex symplectic group S P(2n) with non-Levi isotropy subgroups through an operator realization on highest weight modules over the quantum group Uq ( sp(2n) ) .