Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1503-31
Keywords
Locally graded minimal non-metahamiltonian, soluble, metabelian, $d$-maximal
First Page
1140
Last Page
1143
Recommended Citation
ATLIHAN, S (2017). A note on locally graded minimal non-metahamiltonian groups. Turkish Journal of Mathematics 41 (5): 1140-1143. https://doi.org/10.3906/mat-1503-31
