Finite groups with specific numbers of cyclic subgroups satisfy solvability or supersolvability, with a partial extension of the classification of n-cyclic groups for n at least 13.
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Solvability of Groups via Cyclic Subgroup Count
Finite groups with specific numbers of cyclic subgroups satisfy solvability or supersolvability, with a partial extension of the classification of n-cyclic groups for n at least 13.