Turkish Journal of Mathematics
Abstract
We characterize finite groups with exactly two nonabelian proper subgroups. When $G$ is nilpotent, we show that $G$ is either the direct product of a minimal nonabelian $p$-group and a cyclic $q$-group or a $2$-group. When $G$ is nonnilpotent supersolvable group, we obtain the presentation of $G$. Finally, when $G$ is nonsupersolvable, we show that $G$ is a semidirect product of a $p$-group and a cyclic group.
DOI
10.3906/mat-2105-68
Keywords
Finite groups, minimal nonabelian groups, minimal nonnilpotent groups, critical groups
First Page
2393
Last Page
2405
Recommended Citation
TAERI, B, & BEYG, F. T (2021). Finite groups with three non-abelian subgroups. Turkish Journal of Mathematics 45 (6): 2393-2405. https://doi.org/10.3906/mat-2105-68
