20F99 03E75 2 20K99 2 partition of a group 2 20F05 1 Hirsch-Zaitsev rank 1 P-small 1 Soluble group 1 \(k\)-thin subsets of groups 1 chain conditions 1 cohomological dimension 1 factorized group 1 generalized radical group 1 k-thin subsets of a group 1 minimax group 1 minimax rank 1 product of groups 1 radical group 1 small 1 sparse subset of a group 1 splitting theorems 1 stable soluble group 1 weak chain conditions 1