Search results for "fc-groups"
showing 2 items of 2 documents
On the WGSC Property in Some Classes of Groups
2009
The property of quasi-simple filtration (or qsf) for groups has been introduced in literature more than 10 years ago by S. Brick. This is equivalent, for groups, to the weak geometric simple connectivity (or wgsc). The main interest of these notions is that there is still not known whether all finitely presented groups are wgsc (qsf) or not. The present note deals with the wgsc property for solvable groups and generalized FC-groups. Moreover, a relation between the almost-convexity condition and the Tucker property, which is related to the wgsc property, has been considered for 3-manifold groups.
Groups with soluble minimax conjugate classes of subgroups
2008
A classical result of Neumann characterizes the groups in which each subgroup has finitely many conjugates only as central-by-finite groups. If $\mathfrak{X}$ is a class of groups, a group $G$ is said to have $\mathfrak{X}$-conjugate classes of subgroups if $G/core_G(N_G(H)) \in \mathfrak{X}$ for each subgroup $H$ of $G$. Here we study groups which have soluble minimax conjugate classes of subgroups, giving a description in terms of $G/Z(G)$. We also characterize $FC$-groups which have soluble minimax conjugate classes of subgroups.