# Minimal non-FC-groups and coprime automorphisms of quasi-simple groups

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2004
Ersoy, Kıvanç
A group G is called an FC-group if the conjugacy class of every element is finite. G is called a minimal non-FC-group if G is not an FC-group, but every proper subgroup of G is an FC-group. The first part of this thesis is on minimal non-FC-groups and their finitary permutational representations. Belyaev proved in 1998 that, every perfect locally finite minimal non-FC-group has non-trivial finitary permutational representation. In Chapter 3, we write the proof of Belyaev in detail. Recall that a group G is called quasi-simple if G is perfect and G/Z(G) is simple. The second part of this thesis is on finite quasi-simple groups and their coprime automorphisms. In Chapter 4, the result of Parker and Quick is written in detail: Namely; if Q is a quasi-simple group and A is a non-trivial group of coprime automorphisms of Q satisfying

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Citation Formats
K. Ersoy, “Minimal non-FC-groups and coprime automorphisms of quasi-simple groups,” M.S. - Master of Science, Middle East Technical University, 2004.