Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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2-ENGELIZER SUBGROUP OF A 2-ENGEL TRANSITIVE GROUPS

  • Moghaddam, Mohammad Reza R. (Department of Mathematics Khayyam University, Centre of Excellence in Analysis on Algebraic Structures Ferdowsi University of Mashhad) ;
  • Rostamyari, Mohammad Amin (International Campus Faculty of Mathematical Sciences Ferdowsi University of Mashhad)
  • Received : 2014.10.23
  • Published : 2016.05.31
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Abstract

A general notion of ${\chi}$-transitive groups was introduced by C. Delizia et al. in [6], where ${\chi}$ 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 ${\chi}$-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 ${\chi}$-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 $E^2(G)$. Then we construct the possible values of ${\mid}E^2(G){\mid}$.

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References

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