Contents
Introduction.................................................................................................................... 3
1. Preliminaries (topology & measure).................................................................... 3
2. Problems and the theorem.................................................................................... 7
3. Preliminaries (abstract groups, Cartesian products)....................................... 9
4. Preliminaries (automorphisms, duality theory).................................................. 13
5. Compact groups....................................................................................................... 15
6. Theorems on the groups $D_p$........................................................................... 18
7. A decomposition of compact groups.................................................................... 27
8. Groups in which all compact topologies are isomorphic................................ 33
9. The class M............................................................................................................... 40
10. Proof of the Main Theorem (groups of the class M)........................................ 42
11. Proof of tho Main Theorem (reduced groups).................................................. 47
12. Proof of the Main Theorem (conclusion)........................................................... 48
References.................................................................................................................... 57