Groups with a conjugacy class that is the difference of two normal subgroups
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912983738744832 |
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| author | Lewis, Mark L. Morotti, Lucia Pacifici, Emanuele Sanus, Lucia Tong-Viet, Hung P. |
| author_facet | Lewis, Mark L. Morotti, Lucia Pacifici, Emanuele Sanus, Lucia Tong-Viet, Hung P. |
| contents | We consider finite groups having a conjugacy class that is the difference of two normal subgroups. That is, suppose $G$ is a group and $M$ and $N$ are normal subgroups so that $N < M$, and suppose that there is an element $g \in G$ so that the conjugacy class of $g$ is $M \setminus N$. We find a character-theoretic characterization of this condition, and we determine some structural properties of groups with such a conjugacy class. If we add the condition that $M/N$ is the unique minimal normal subgroup of $G/N$, then we obtain a generalization of a result by S.M. Gagola. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Groups with a conjugacy class that is the difference of two normal subgroups Lewis, Mark L. Morotti, Lucia Pacifici, Emanuele Sanus, Lucia Tong-Viet, Hung P. Group Theory Primary 20C15, Secondary 20D06, 20D10 We consider finite groups having a conjugacy class that is the difference of two normal subgroups. That is, suppose $G$ is a group and $M$ and $N$ are normal subgroups so that $N < M$, and suppose that there is an element $g \in G$ so that the conjugacy class of $g$ is $M \setminus N$. We find a character-theoretic characterization of this condition, and we determine some structural properties of groups with such a conjugacy class. If we add the condition that $M/N$ is the unique minimal normal subgroup of $G/N$, then we obtain a generalization of a result by S.M. Gagola. |
| title | Groups with a conjugacy class that is the difference of two normal subgroups |
| topic | Group Theory Primary 20C15, Secondary 20D06, 20D10 |
| url | https://arxiv.org/abs/2603.25407 |