2-ENGELIZER SUBGROUP OF A 2-ENGEL TRANSITIVE GROUPS

Title & Authors
2-ENGELIZER SUBGROUP OF A 2-ENGEL TRANSITIVE GROUPS

Abstract
A general notion of $\small{{\chi}}$-transitive groups was introduced by C. Delizia et al. in [6], where $\small{{\chi}}$ is a class of groups. In [5], Ciobanu, Fine and Rosenberger studied the relationship among the notions of conjugately separated abelian, commutative transitive and fully residually $\small{{\chi}}$-groups. In this article we study the concept of 2-Engel transitive groups and among other results, its relationship with conjugately separated 2-Engel and fully residually $\small{{\chi}}$-groups are established. We also introduce the notion of 2-Engelizer of the element x in G and denote the set of all 2-Engelizers in G by $\small{E^2(G)}$. Then we construct the possible values of $\small{{\mid}E^2(G){\mid}}$.
Keywords
2-ET group;$\small{CSE^2}$-group;residually $\small{{\chi}}$-group;fully residually $\small{{\chi}}$-group;2-Engelizer subgroup;
Language
English
Cited by
References
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