Two Theorems about Nilpotent Subgroup

Two Remarks about Nilpotent Operators of Order Two

We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a complex symmetric operator. In fact, we prove that this property characterizes nilpotents of order two among all nonzero bounded operators. Second, we establish...

Two theorems about Galiukschov semicontextual languages

We assume the reader familiar with the basic notions of formal language theory (from [3], for example) and we specify only some notions about the semicontextual grammars introduced in [1], under linguistic motivations. A semicontextual grammar is a triple G = (V, B, P), where V is a nonempty finite alphabet, B is a finite language over V and P is a finite set of rewriting rules of the form xy -...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Normal subgroup growth in free class-2-nilpotent groups

Let F2,d denote the free class-2-nilpotent group on d generators. We compute the normal zeta functions ζ F2,d(s), prove that they satisfy local functional equations and determine their abscissae of convergence and pole orders.

Citations about Gödel’s Theorems

This is a short account of various notes and opinions about Gödel’s theorems I found in my books. It should ease the task of actually writing something about Gödel’s First Incompleteness Theorem. Citations about Gödel’s Theorems