Locally Fınıte Groups Wıth All Subgroups Subnormal Or Nılpotent-By-Chernġkov

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Thesis Type: Postgraduate

Institution Of The Thesis: Gazi University, Turkey

Approval Date: 2016

Thesis Language: Turkish

Student: Aykut Kayhan

Supervisor: AYNUR ARIKAN

Abstract:

In this thesis, the paper written by Howard SMITH named Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov is studied. Let G is locally finite group satisfying all subgroups subnormal or nilpotent-by-Chernikov. It is shown that if G is finite exponent; then G is nilpotent-by-finite. Moreover, it is shown that if G is not nilpotent-by- Chernikov, then G has a section isomorphic to a group G(F,K) = A ⋊ K such that A and K is respectively additive and multicaptive subgroup of locally finite F field or that G(F,K) is elementary abelian p-group. In particular, K generates F by acting on A by multicaption.