Virtually solvable group
= Virtually solvable group
= Virtually soluble group
{synonym}
A <group> is virtually solvable, or virtually soluble, when it contains a <solvable group> as a <finite-index subgroup>. This is preserved under <subgroups>, quotients and <group extensions>. The extension proof can use a <finite-index characteristic soluble subgroup> of the kernel, followed by centralizing the resulting finite normal kernel. Finite generation is not required for these closure properties.