A_t-groups With Few Non-A_t-i-subgroups Of Index Pⁱ

A finite p-group G is called an A_t-group,if all subgroups of index pt are abelian and at least one subgroup of index p1-1 is not abelian.In this paper,we classify the A_t-groups in which the numbers all of whose non-A_t-i-subgroups of index pi are at most p and the A_t-groups all of non-A_t-i-subgroups of index pi are cyclic,respectively.And the A_t-groups all of non-A_t-i-subgroups of index pi are abelian are characterized.