The authors study linear groups of infinite central dimension and of infinite p-rank all of whose proper subgroups of infinite p-rank are of finite central dimension.

We study a ZG-module A in the case where the group G is locally solvable and satisfies the condition min-naz and its cocentralizer in A is not an Artinian Z-module. We prove that the group G is solvable under the conditions indicated above. The structure of the group G is studied in detail in the case where this group is not a Chernikov group.

Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class.

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