Squares of real conjugacy classes in finite groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929238256386048 |
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| author | Beltrán, Antonio Felipe, María José Melchor, Carmen |
| author_facet | Beltrán, Antonio Felipe, María José Melchor, Carmen |
| contents | We prove that if a finite group $G$ contains a conjugacy class $K$ whose square is of the form $1 \cup D$, where $D$ is a conjugacy class of $G$, then $\langle K \rangle$ is a solvable proper normal subgroup of $G$ and we completely determine its structure. We also obtain the structure of those groups in which the assumption above is true for all non-central conjugacy classes and when every conjugacy class satisfies that its square is the union of all central conjugacy classes except at most one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Squares of real conjugacy classes in finite groups Beltrán, Antonio Felipe, María José Melchor, Carmen Group Theory We prove that if a finite group $G$ contains a conjugacy class $K$ whose square is of the form $1 \cup D$, where $D$ is a conjugacy class of $G$, then $\langle K \rangle$ is a solvable proper normal subgroup of $G$ and we completely determine its structure. We also obtain the structure of those groups in which the assumption above is true for all non-central conjugacy classes and when every conjugacy class satisfies that its square is the union of all central conjugacy classes except at most one. |
| title | Squares of real conjugacy classes in finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2402.06243 |