University of Isfahan International Journal of Group Theory 2251-7650 2 3 2013 09 01 A note on finite C-tidy groups 9 17 2009 10.22108/ijgt.2013.2009 EN Sekhar Jyoti Baishya North-eastern Hill University Journal Article 2012 10 02 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 $K(G)=\lbrace 1 \rbrace$‎. https://ijgt.ui.ac.ir/article_2009_40492b1ec662d802b7e99ceac68fc720.pdf