Landau's theorem on conjugacy classes for normal subgroups

@article{Beltrn2016LandausTO,
  title={Landau's theorem on conjugacy classes for normal subgroups},
  author={Antonio Beltr{\'a}n and Mar{\'i}a Jos{\'e} Felipe and Carmen Melchor},
  journal={IJAC},
  year={2016},
  volume={26},
  pages={1453-1466}
}
Landau’s theorem on conjugacy classes asserts that there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes for any positive integer k. We show that, for any positive integers n and s, there exist finitely many finite groups G, up to isomorphism, having a normal subgroup N of index n which contains exactly s non-central G-conjugacy classes. Upper bounds for the orders of G and N are obtained; we use these bounds to classify all finite groups with normal… CONTINUE READING

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