On a Class of Groups with Lagrangian Factor Groups

Fernando Tuccillo

Abstract: We classify the 2-dual minimal non supersoluble groups, whose factor groups satisfy the converse of the Lagrange's theorem. From this classification we deduce that there is no upper bound for the 3-rank, as for the 2-rank, of a group with lagrangian factor groups. We conjecture that the groups with lagrangian factor groups are $p$-supersoluble, for each prime $p\ne2,3$.

Keywords: The converse Lagrange's theorem; groups with lagrangian factor groups.

Classification (MSC2000): 20D10

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