Finite groups with star-free noncyclic graphs
For a finite noncyclic group , let Cyc( ) be the set of elements of such that 〈 , 〉 is cyclic for each of . The noncyclic graph of is a graph with the vertex set ∖ Cyc( ), having an edge between two distinct vertices and if 〈 , 〉 is not cyclic. In this paper, we classify all finite noncyclic groups...
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| Veröffentlicht in: | Open mathematics (Warsaw, Poland) Poland), 2019-08, Vol.17 (1), p.906-912 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | For a finite noncyclic group
, let Cyc(
) be the set of elements
of
such that 〈
,
〉 is cyclic for each
of
. The noncyclic graph of
is a graph with the vertex set
∖ Cyc(
), having an edge between two distinct vertices
and
if 〈
,
〉 is not cyclic. In this paper, we classify all finite noncyclic groups whose noncyclic graphs are
-free, where
is a star and 3 ≤
≤ 6. |
|---|---|
| ISSN: | 2391-5455 2391-5455 |
| DOI: | 10.1515/math-2019-0071 |