Turkish Journal of Mathematics
DOI
10.3906/mat-1503-31
Abstract
We prove that a nonperfect locally gradedminimal non-metahamiltonian group $G$ is a soluble group withderived length of at most 4. On the other hand, if $G$ is perfect,then $G/\Phi (G)$ is isomorphic to $A_{5}$, where $\Phi (G)$ isthe Frattini subgroup of $G$ and $A_{5}$ is the alternating group.Moreover, we show that under some conditions,if G is a $p$-group, then G is metabelian, where $p$ is a prime integer.
Keywords
Locally graded minimal non-metahamiltonian, soluble, metabelian, $d$-maximal
First Page
1140
Last Page
1143
Recommended Citation
ATLIHAN, SEVGİ
(2017)
"A note on locally graded minimal non-metahamiltonian groups,"
Turkish Journal of Mathematics: Vol. 41:
No.
5, Article 5.
https://doi.org/10.3906/mat-1503-31
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss5/5
