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 |Q: C_{Q}(A)| < / n then |Q| < / n3,
that is |Q| is bounded by a function of n.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12605262/index.pdf |
| Date | 01 September 2004 |
| Creators | Ersoy, Kivanc |
| Contributors | Kuzucuoglu, Mahmut |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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