The Cyclic Graph of a $2$-Frobenius Group
The cyclic graph of a group $G$ is the graph whose vertices are the nonidentity elements of $G$ and whose edges connect distinct elements $x$ and $y$ if and only if the subgroup $\langle x,y\rangle$ is cyclic. We obtain information about the cyclic graph of $2$-Frobenius groups. The cyclic graph of...
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| creator | Costanzo, David G Lewis, Mark L |
| description | The cyclic graph of a group $G$ is the graph whose vertices are the
nonidentity elements of $G$ and whose edges connect distinct elements $x$ and
$y$ if and only if the subgroup $\langle x,y\rangle$ is cyclic. We obtain
information about the cyclic graph of $2$-Frobenius groups. The cyclic graph of
a $2$-Frobenius group is disconnected. In this paper, we determine the number
of connected components of the cyclic graph of any $2$-Frobenius group. |
| doi_str_mv | 10.48550/arxiv.2103.15574 |
| format | Article |
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nonidentity elements of $G$ and whose edges connect distinct elements $x$ and
$y$ if and only if the subgroup $\langle x,y\rangle$ is cyclic. We obtain
information about the cyclic graph of $2$-Frobenius groups. The cyclic graph of
a $2$-Frobenius group is disconnected. In this paper, we determine the number
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nonidentity elements of $G$ and whose edges connect distinct elements $x$ and
$y$ if and only if the subgroup $\langle x,y\rangle$ is cyclic. We obtain
information about the cyclic graph of $2$-Frobenius groups. The cyclic graph of
a $2$-Frobenius group is disconnected. In this paper, we determine the number
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nonidentity elements of $G$ and whose edges connect distinct elements $x$ and
$y$ if and only if the subgroup $\langle x,y\rangle$ is cyclic. We obtain
information about the cyclic graph of $2$-Frobenius groups. The cyclic graph of
a $2$-Frobenius group is disconnected. In this paper, we determine the number
of connected components of the cyclic graph of any $2$-Frobenius group.</abstract><doi>10.48550/arxiv.2103.15574</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Group Theory |
| title | The Cyclic Graph of a $2$-Frobenius Group |
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