Locally finite groups house sylow subgroups are Chernikov

11 LOCALLY FINITE GROUPS WHOSE SYLOW SUBGROUPS ARE CHERNIKOV ( Master Thesis ) Yasemin KIYMAZ GAZİ UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY May -2001 ABSTRACT In this work we have considered the B. Hartley's paper entitled "Locally finite groups whose Sylow subgroups are Chernikov" which was introduced in the Group Theory Conference in 1994 in Ravello, Italy; M.R. Dixon and M. J. Tomkinson's paper entitled "The local conjugacy of some Sylow bases in a class of locally finite groups" and a part of preprint of S. D. Bell's Ph.D. thesis entitled "Uncountable locally finite groups with Chernikov Sylow subgroups". Bear's conjecture "Let G be a countable -ST-group. Then G has a proper basis subgroup if and only if G is not hyperfinite." is proved by V.V. Belyaev and S.D.Bell independently, in some cases. We give the complete proof of V.V. Belyaev and a summary of the proof of S.D.Bell. Science Code : 4030100 Key Words : Locally Finite Group, Hyperfinite Group, Min-p Condition, Co-Hopfian, Basis Subgroup. Page Number : 61 Supervisor : Yrd. Doç. Dr. Ahmet ARIKAN