On finite solvable linear groups

Undistorted Solvable Linear Groups

We discuss distortion of solvable linear groups over a locally compact field and provide necessary and sufficient conditions for a subgroup to be undistorted when the field is of characteristic zero.

finite bci-groups are solvable

‎let $s$ be a subset of a finite group $g$‎. ‎the bi-cayley graph ${rm bcay}(g,s)$ of $g$ with respect to $s$ is an undirected graph with vertex set $gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin g‎, ‎ sin s}$‎. ‎a bi-cayley graph ${rm bcay}(g,s)$ is called a bci-graph if for any bi-cayley graph ${rm bcay}(g,t)$‎, ‎whenever ${rm bcay}(g,s)cong {rm bcay}(g,t)$ we have $t=gs^alpha$ for some $...

Random walks on finite rank solvable groups

Abstract. We establish the lower bound p2t(e, e) exp(−t1/3), for the large times asymptotic behaviours of the probabilities p2t(e, e) of return to the origin at even times 2t, for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r , such that any of its finitely generated subgroup admit...

Engel-like Identities Characterizing Finite Solvable Groups

Counting homomorphisms onto finite solvable groups

We present a method for computing the number of epimorphisms from a finitely presented group G to a finite solvable group Γ, which generalizes a formula of Gaschütz. Key to this approach are the degree 1 and 2 cohomology groups of G, with certain twisted coefficients. As an application, we count low-index subgroups of G. We also investigate the finite solvable quotients of the Baumslag-Solitar ...