فهرست نشریات علمی دسترسی آزاد ایران

Let $\Gamma$ be a finite group. A subgroup $H$ of $\Gamma$ is called ``fully liftable" in $\Gamma$ if every automorphism of $H$ is the restriction of an automorphism of $\Gamma$. Let $G=C_{p^{k_1}}\times C_{p^{k_2}}$, where $1\le k_1\le k_2$ and $p$ is prime. Using information about the subgroup structure of $G$ and knowledge of ${\rm Aut}(G)$, we characterize all fully liftable subgroups of $G$. It turns out that all cyclic subgroups of $G$ are fully liftable, and non-cyclic subgroups are fully liftable if and only if they are automorphic to certain subproducts of $G$, where two subgroups $H$ and $K$ are automorphic in $G$ if there exists $\alpha\in{\rm Aut}(G)$ such that $\alpha(H)=K$. Further, we compare the fully liftable subgroups of $G$ with the characteristic subgroups of $G$, which are similarly characterized by certain subproducts. Finally, we exhibit some interesting lattice features of both fully liftable subgroups of $G$ and characteristic subgroups of $G$.