Frattini Subgroups in Finitely Generated Linear Groups

Commutator Length of Finitely Generated Linear Groups

The commutator length “cl G ” of a group G is the least natural number c such that every element of the derived subgroup of G is a product of c commutators. We give an upper bound for cl G when G is a d-generator nilpotent-by-abelian-by-finite group. Then, we give an upper bound for the commutator length of a soluble-by-finite linear group over C that depends only on d and the degree of lineari...

On Intersections of Finitely Generated Subgroups of Free Groups

and asked if the factor 2 can be dropped. If one translates her approach (which is a slight modification of Howson's) to graph-theoretic terms, it easily shows that the answer is often "yes"in fact, for most U the answer is "yes" for all V. According to Gersten [G], the above problem has come to be known as the "Haana Neumann Conjecture." Using ideas of immersions of graphs originating from Sta...

Abelian groups have/are near Frattini subgroups

The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.