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A note on finite C-tidy groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 2، شماره 3، آذر 2013، صفحه 9-17 اصل مقاله (414.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2009 | ||
| نویسنده | ||
| Sekhar Jyoti Baishya* | ||
| North-eastern Hill University | ||
| چکیده | ||
| Let $G$ be a group and $x \in G$. The cyclicizer of $x$ is defined to be the subset $Cyc(x)=\lbrace y \in G \mid \langle x, y\rangle \; {\rm is \; cyclic} \rbrace$. $G$ is said to be a tidy group if $Cyc(x)$ is a subgroup for all $x \in G$. We call $G$ to be a C-tidy group if $Cyc(x)$ is a cyclic subgroup for all $x \in G \setminus K(G)$, where $K(G)$ is the intersection of all the cyclicizers in $G$. In this note, we classify finite C-tidy groups with $K(G)=\lbrace 1 \rbrace$. | ||
| کلیدواژهها | ||
| Finite groups؛ cyclicizers؛ tidy groups؛ C-tidy groups | ||
| مراجع | ||
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