Totally imprimitive p-groups satisfying the cyclic-block property are investigated. It is shown that in these groups any two blocks either are disjoint or one is contained in the other, and so the set of all blocks of the same size forms just one block system. Furthermore the non-FC-subgroups of these groups are transitive. For each prime p totally imprimitive p-subgroups of FSym(ℕ*) satisfying the cyclic-block property are constructed, which are not minimal non-FC-groups.
© de Gruyter 2011