On the Finiteness length of some soluble linear groups

on the effect of linear & non-linear texts on students comprehension and recalling

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NSE characterization of some linear groups

‎For a finite group $G$‎, ‎let $nse(G)={m_kmid kinpi_e(G)}$‎, ‎where $m_k$ is the number of elements of order $k$ in $G$‎ ‎and $pi_{e}(G)$ is the set of element orders of $G$‎. ‎In this paper‎, ‎we prove that $Gcong L_m(2)$ if and only if $pmid |G|$ and $nse(G)=nse(L_m(2))$‎, ‎where $min {n,n+1}$ and $2^n-1=p$ is a prime number.

Finiteness properties of soluble arithmetic groups over global function fields

Let G be a Chevalley group scheme and B ≤ G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K , and OS be the corresponding S–arithmetic ring. Then, the S– arithmetic group B(OS) is of type F |S|−1 but not of type FP |S| . Moreover one can derive lower and upper bounds for the geometric invariants Σ(B(OS)). These are sha...

Finiteness Properties of Some Groups of Local Similarities

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson’s group V . Guided by previous work on Thompson’s group V , we establish a number of new results about FSS groups. Our main result is that a class of FSS groups are of type F∞. This generalizes ...

Absolute Fourth Moments and Finiteness Of Linear Groups