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THE CYCLIC GRAPH OF A Z-GROUP
Published online by Cambridge University Press: 14 December 2020
Abstract
For a group G, we define a graph
$\Delta (G)$
by letting
$G^{\scriptsize\#}=G\setminus {\{\,1\,\}} $
be the set of vertices and by drawing an edge between distinct elements
$x,y\in G^{\scriptsize\#}$
if and only if the subgroup
$\langle x,y\rangle $
is cyclic. Recall that a Z-group is a group where every Sylow subgroup is cyclic. In this short note, we investigate
$\Delta (G)$
for a Z-group G.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 295 - 301
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
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