Doubly Sequenceable Groups
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909155070050304 |
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| author | Javaheri, Mohammad |
| author_facet | Javaheri, Mohammad |
| contents | Given a sequence ${\bf g}: g_0,\ldots, g_{m}$, in a finite group $G$ with $g_0=1_G$, let ${\bf \bar g}: \bar g_0,\ldots, \bar g_{m}$, be the sequence defined by $\bar g_0=1_G$ and $\bar g_i=g_{i-1}^{-1}g_i$ for $1\leq i \leq m$. We say that $G$ is doubly sequenceable if there exists a sequence ${\bf g}$ in $G$ such that every element of $G$ appears exactly twice in each of ${\bf g}$ and ${\bf \bar g}$. If a group $G$ is abelian, odd, sequenceable, R-sequenceable, or terraceable, then $G$ is doubly sequenceable. In this paper, we show that if $N$ is an odd or sequenceable group and $H$ is an abelian group, then $N \times H$ is doubly sequenceable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14334 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Doubly Sequenceable Groups Javaheri, Mohammad Group Theory Number Theory 20K01, 05E15 (Primary), 05B30, 20D15, 20F22 (Secondary) Given a sequence ${\bf g}: g_0,\ldots, g_{m}$, in a finite group $G$ with $g_0=1_G$, let ${\bf \bar g}: \bar g_0,\ldots, \bar g_{m}$, be the sequence defined by $\bar g_0=1_G$ and $\bar g_i=g_{i-1}^{-1}g_i$ for $1\leq i \leq m$. We say that $G$ is doubly sequenceable if there exists a sequence ${\bf g}$ in $G$ such that every element of $G$ appears exactly twice in each of ${\bf g}$ and ${\bf \bar g}$. If a group $G$ is abelian, odd, sequenceable, R-sequenceable, or terraceable, then $G$ is doubly sequenceable. In this paper, we show that if $N$ is an odd or sequenceable group and $H$ is an abelian group, then $N \times H$ is doubly sequenceable. |
| title | Doubly Sequenceable Groups |
| topic | Group Theory Number Theory 20K01, 05E15 (Primary), 05B30, 20D15, 20F22 (Secondary) |
| url | https://arxiv.org/abs/2208.14334 |