let $g$ be a group and $x in g$. the cyclicizer of $x$ is defined to be the subset $cyc(x)=lbrace y in g mid langle x, yrangle ; {rm is ; cyclic} rbrace$. $g$ 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 ...
