Solvable Generation of Finite Groups

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 $...

Parallel Construction of Finite Solvable Groups

An algorithm for the construction of nite solvable groups of small order is given. A parallelized version under PVM is presented. Diierent models for parallelization are discussed. A nite group G is called solvable, if there exists a chain of normal subgroups

Finite subnormal coverings of certain solvable groups

A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...

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 ...