Guardat en:
| Autors principals: | , , |
|---|---|
| Format: | Preprint |
| Publicat: |
2024
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2402.06708 |
| Etiquetes: |
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Taula de continguts:
- 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 exists only a finite number of finite groups $G$, up to isomorphism, having a normal subgroup $N$ of index $n$ which contains exactly $s$ non-central $G$-conjugacy classes. We provide upper bounds for the orders of $G$ and $N$, which are used by using GAP to classify all finite groups with normal subgroups having a small index and few $G$-classes. We also study the corresponding problems when we only take into account the set of $G$-classes of prime-power order elements contained in a normal subgroup.