‎In a previous paper‎, ‎the second author established that‎, ‎given finite fields $F

‎Quasinormal subgroups have been studied for nearly 80 years‎. ‎In finite groups‎, ‎questions concerning them invariably reduce to $p$-groups‎, ‎and here they have the added interest of being invariant under projectivities‎, ...

We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the ‎characteristic. Namely, we prove the following. Let $kappa$ be an infinite cardinal. If $G=underset{i=1}{ ...