Turkish Journal of Mathematics
DOI
10.3906/mat-2105-68
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.
Keywords
Finite groups, minimal nonabelian groups, minimal nonnilpotent groups, critical groups
First Page
2393
Last Page
2405
Recommended Citation
TAERI, BIJAN and BEYG, FATEMEH TAYANLOO
(2021)
"Finite groups with three non-abelian subgroups,"
Turkish Journal of Mathematics: Vol. 45:
No.
6, Article 3.
https://doi.org/10.3906/mat-2105-68
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss6/3
