The finite p-groups with p conjugacy classes of non-normal subgroups
Tóm tắt
Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. The finite groups for which ν(G) ≤ 2 were determined by Dedekind and by Schmidt in the early times of group theory. On the other hand, if G is a finite p-group, La Haye and Rhemtulla have proved that either ν(G) ≤ 1 or ν(G) ≥ p. In this note, we determine all finite p-groups satisfying ν(G) = p for p > 2.
Tài liệu tham khảo
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