Subnomality in soluble minimax groups

groups with soluble minimax conjugate classes of subgroups

a classical result of neumann characterizes the groups in which each subgroup has finitely many conjugates only as central-by-finite groups. if x is a class of groups, a group g is said to have x-conjugate classes of subgroups if g/coreg(ng(h)) 2 x for each subgroup h of g. here we study groups which have soluble minimax conjugate classes of subgroups, giving a description in terms of g/z(g). w...

groups with minimax commutator subgroup

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

Expansion in Soluble Groups

Soluble omega-categorical groups

Isoperimetric inequalities for soluble groups

We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic.