a note on finite c-tidy groups
نویسندگان
چکیده
let $g$ be a group and $x in g$. the cyclicizer of $x$ is defined to be the subset $cyc(x)=lbrace y in g mid langle x, yrangle ; {rm is ; cyclic} rbrace$. $g$ 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 $g$. in this note, we classify finite c-tidy groups with $k(g)=lbrace 1 rbrace$.
منابع مشابه
on finite c-tidy groups
a group $g$ is said to be a c-tidy group if for every element $x in g setminus k(g)$, the set $cyc(x)=lbrace y in g mid langle x, y rangle ; {rm is ; cyclic} rbrace$ is a cyclic subgroup of $g$, where $k(g)=underset{x in g}bigcap cyc(x)$. in this short note we determine the structure of finite c-tidy groups.
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عنوان ژورنال:
international journal of group theoryناشر: university of isfahan
ISSN 2251-7650
دوره 2
شماره 3 2012
کلمات کلیدی
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