On some types of antinormal subgroups

Abstract

A subgroup $$$H$$$ is called a pronormal subgroup in a group $$$G$$$ if for any $$$g \in G$$$ subgroups $$$H$$$ and $$$H^g$$$ are conjugated in $$${<}H, H^g{>}$$$. A subgroup $$$H$$$ is called a contranormal subgroup in a group $$$G$$$ if $$$H^G = G$$$. A subgroup $$$H$$$ is called a weak pronormal subgroup in a group $$$G$$$ if $$$N_K(H)$$$ is contranormal in any subgroup $$$K$$$ which contains $$$H$$$. We obtained the examples of non pronormal but weak pronormal subgroups.