On $k$-submodular subgroups of finite groups
On $k$-submodular subgroups of finite groups
Let $n$ be a natural number. A subgroup $H$ of a group $G$ will be called $n$-modularly embedded in $G$ if either $H$ is normal in $G$ or $H\not= \mathrm{Core}_{G}(H)$, $|G:H| =p$ and $|G/\mathrm{Core}_{G}(H)|=pq^{n}$, $q^{n}$ divides $p-1$ for some primes $p$ and $q$. Let $k$ be a fixed natural number. …