A note on finite C-tidy groups

Document Type: Research Paper

Author

North-eastern Hill University

Abstract

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 $K(G)=\lbrace 1 \rbrace$‎.

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References

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