Centralizers in the diagonal direct limits of the symmetric groups and of the monomial groups

Centralizers of finite subgroups in the direct limit of the finite and finitary symmetric groups via strictly diagonal embeddings is characterized in 2015 by Güven, Kegel and Kuzucuoğlu. In this paper this idea is extended to the case of diagonal embeddings. In addition, a new class of infinite limit monomial groups is constructed via diagonal embedding.