A set theoretic version of equations on groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911549768073216 |
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| author | Lazorec, Mihai-Silviu |
| author_facet | Lazorec, Mihai-Silviu |
| contents | Let $G$ be a finite group. The aim of this paper is to study the number of solutions $S\subseteq G$ of the equation $\mho^{\{n\}}(S)=L$, where $L$ is a non-empty subset of $G$, $n$ is a positive integer and $\mho^{\{n\}}(S)=\{ s^n \ | \ s\in S\}$. Besides our findings obtained in this general frame, we also outline some results which hold for some particular cases such as: \textit{i)} $L$ is a normal subset of $G$; \textit{ii)} $G$ is abelian; \textit{iii)} $G$ is an extraspecial $p$-group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A set theoretic version of equations on groups Lazorec, Mihai-Silviu Group Theory Let $G$ be a finite group. The aim of this paper is to study the number of solutions $S\subseteq G$ of the equation $\mho^{\{n\}}(S)=L$, where $L$ is a non-empty subset of $G$, $n$ is a positive integer and $\mho^{\{n\}}(S)=\{ s^n \ | \ s\in S\}$. Besides our findings obtained in this general frame, we also outline some results which hold for some particular cases such as: \textit{i)} $L$ is a normal subset of $G$; \textit{ii)} $G$ is abelian; \textit{iii)} $G$ is an extraspecial $p$-group. |
| title | A set theoretic version of equations on groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2603.27026 |